Original tone mapped image by Camera {x=middle, c=1}:

Histogram of the tone mapped image:

Image statistics of the tone-mapped image:

Median percentile of the lightness (CIE L*a*b*): 26.3719
Mean of the chroma value (CIE L*a*b*): 7.9925
Image produced by the generic tone mapping operator:
(evalution of the fit via PSNR: PSNR = 37.3059dB)

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: 0.69615
Contrast: 1.5781
Low midtone range: 1.4644
High midtone range: 1.079
Saturation: 0.41797
Frequencies: 0.77, 0.946, 0.992, 0.994, 0.995