Original tone mapped image by Camera {x=middle, c=1.8}:

Histogram of the tone mapped image:

Image statistics of the tone-mapped image:

Median percentile of the lightness (CIE L*a*b*): 27.6317
Mean of the chroma value (CIE L*a*b*): 13.4223
Image produced by the generic tone mapping operator:
(evalution of the fit via PSNR: PSNR = 35.0373dB)

Fitted tone curve of the generic tone mapping operator,
compared to the luminance compression done by the tone mapping operator:

Fitted parameters of the generic tmo:

Exposure: 0.65991
Contrast: 1.6495
Low midtone range: 1.4766
High midtone range: 1.2508
Saturation: 0.67901
Frequencies: 0.771, 0.959, 1.01, 1.007, 1.015