Average Error: 0.1 → 0.0
Time: 7.3s
Precision: binary32
Cost: 9760
\[0 \leq s \land s \leq 1.0651631\]
\[\frac{1}{1 + e^{\frac{-x}{s}}} \]
↓
\[e^{-\mathsf{log1p}\left(e^{\frac{-x}{s}}\right)} \]
(FPCore (x s) :precision binary32 (/ 1.0 (+ 1.0 (exp (/ (- x) s)))))
↓
(FPCore (x s) :precision binary32 (exp (- (log1p (exp (/ (- x) s))))))
float code(float x, float s) {
	return 1.0f / (1.0f + expf((-x / s)));
}
↓
float code(float x, float s) {
	return expf(-log1pf(expf((-x / s))));
}

function code(x, s)
	return Float32(Float32(1.0) / Float32(Float32(1.0) + exp(Float32(Float32(-x) / s))))
end
↓
function code(x, s)
	return exp(Float32(-log1p(exp(Float32(Float32(-x) / s)))))
end

\frac{1}{1 + e^{\frac{-x}{s}}}
↓
e^{-\mathsf{log1p}\left(e^{\frac{-x}{s}}\right)}

Error

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. Applied egg-rr0.1

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

  3. Applied egg-rr0.0

    \[\leadsto \color{blue}{e^{-\mathsf{log1p}\left(e^{\frac{-x}{s}}\right)}} \]

  4. Final simplification0.0

    \[\leadsto e^{-\mathsf{log1p}\left(e^{\frac{-x}{s}}\right)} \]

Alternatives

Alternative 1
Error0.1
Cost3456
\[\frac{1}{e^{\frac{-x}{s}} + 1} \]
Alternative 2
Error1.4
Cost516
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq 40:\\ \;\;\;\;\frac{1}{1 + \frac{1}{1 + \frac{x}{s}}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
Alternative 3
Error9.9
Cost196
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq 50:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
Alternative 4
Error20.7
Cost32
\[0.5 \]

Error

Reproduce

herbie shell --seed 2022228 
(FPCore (x s)
  :name "Logistic function"
  :precision binary32
  :pre (and (<= 0.0 s) (<= s 1.0651631))
  (/ 1.0 (+ 1.0 (exp (/ (- x) s)))))