Average Error: 0.1 → 0.1
Time: 4.2s
Precision: binary32
\[0 \leq s \land s \leq 1.0651631\]
\[\frac{1}{1 + e^{\frac{-x}{s}}}\]
↓
\[\frac{1}{1 + e^{\frac{-x}{s}}}\]
\frac{1}{1 + e^{\frac{-x}{s}}}
↓
\frac{1}{1 + e^{\frac{-x}{s}}}
(FPCore (x s) :precision binary32 (/ 1.0 (+ 1.0 (exp (/ (- x) s)))))
↓
(FPCore (x s) :precision binary32 (/ 1.0 (+ 1.0 (exp (/ (- x) s)))))
float code(float x, float s) {
	return 1.0f / (1.0f + expf(-x / s));
}
↓
float code(float x, float s) {
	return 1.0f / (1.0f + expf(-x / s));
}

Error

Bits error versus x

Bits error versus s

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{1}{1 + e^{\frac{-x}{s}}}\]
  2. Using strategy rm

  3. Applied pow1_binary320.1

    \[\leadsto \frac{1}{\color{blue}{{\left(1 + e^{\frac{-x}{s}}\right)}^{1}}}\]

  4. Final simplification0.1

    \[\leadsto \frac{1}{1 + e^{\frac{-x}{s}}}\]

Reproduce

herbie shell --seed 2021175 
(FPCore (x s)
  :name "Logistic CDF"
  :precision binary32
  :pre (<= 0.0 s 1.0651631)
  (/ 1.0 (+ 1.0 (exp (/ (- x) s)))))