Average Error: 0.2 → 0.2

Time: 1.8s

Precision: binary64

could not determine a ground truth for program body (more)
1. x = 127140.91663662092

\[\log \left(1 - \frac{1}{1 + e^{-x}}\right)\]

↓

\[\log \left(1 - \frac{1}{1 + e^{-x}}\right)\]

Error

The X axis uses an exponential scale — Bits error versus x

The X axis uses an exponential scale — Bits error versus x

Derivation

Initial program 0.2
\[\log \left(1 - \frac{1}{1 + e^{-x}}\right)\]
Final simplification0.2
\[\leadsto \log \left(1 - \frac{1}{1 + e^{-x}}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(log (- 1 (/ 1 (+ 1 (exp (- x))))))"
  :precision binary64
  (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg x)))))))