Average Error: 0.1 → 0.1
Time: 11.4s
Precision: binary32
Cost: 6656
\[0 \leq s \land s \leq 1.0651631\]
\[\frac{1}{1 + e^{\frac{-x}{s}}} \]
↓
\[\frac{1}{1 + {e}^{\left(\frac{-x}{s}\right)}} \]
(FPCore (x s) :precision binary32 (/ 1.0 (+ 1.0 (exp (/ (- x) s)))))
↓
(FPCore (x s) :precision binary32 (/ 1.0 (+ 1.0 (pow E (/ (- 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 + powf(((float) M_E), (-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 Float32(Float32(1.0) / Float32(Float32(1.0) + (Float32(exp(1)) ^ Float32(Float32(-x) / s))))
end

function tmp = code(x, s)
	tmp = single(1.0) / (single(1.0) + exp((-x / s)));
end
↓
function tmp = code(x, s)
	tmp = single(1.0) / (single(1.0) + (single(2.71828182845904523536) ^ (-x / s)));
end

\frac{1}{1 + e^{\frac{-x}{s}}}
↓
\frac{1}{1 + {e}^{\left(\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-rr0.1

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

  4. Applied egg-rr0.1

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

  5. Final simplification0.1

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

Alternatives

Alternative 1
Error0.1
Cost3456
\[\frac{1}{1 + e^{\frac{-x}{s}}} \]
Alternative 2
Error3.5
Cost740
\[\begin{array}{l} \mathbf{if}\;x \leq -1.999999936531045 \cdot 10^{-20}:\\ \;\;\;\;\frac{1}{2 + \left(0.5 \cdot \left(\frac{1}{s \cdot s} \cdot \frac{x}{\frac{1}{x}}\right) - \frac{x}{s}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + \frac{1}{1 + \frac{x}{s}}}\\ \end{array} \]
Alternative 3
Error3.5
Cost644
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq 100000:\\ \;\;\;\;\frac{1}{1 + \frac{1}{1 + \frac{x}{s}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x \cdot \left(-x\right)}{\frac{2}{\frac{1}{-s \cdot s}}}}\\ \end{array} \]
Alternative 4
Error3.2
Cost580
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq 0.4000000059604645:\\ \;\;\;\;\frac{1}{1 + \frac{1}{1 + \frac{x}{s}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{2 + 0.5 \cdot \left(x \cdot \frac{x}{s \cdot s}\right)}\\ \end{array} \]
Alternative 5
Error3.3
Cost516
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq 0.4000000059604645:\\ \;\;\;\;\frac{1}{1 + \frac{1}{1 + \frac{x}{s}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-2}{x}}{\frac{-x}{s \cdot s}}\\ \end{array} \]
Alternative 6
Error11.9
Cost484
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq 0.4000000059604645:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-2}{x}}{\frac{-x}{s \cdot s}}\\ \end{array} \]
Alternative 7
Error13.3
Cost452
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq 100000:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;s \cdot \left(2 \cdot \frac{s}{x \cdot x}\right)\\ \end{array} \]
Alternative 8
Error13.3
Cost452
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq 0.4000000059604645:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{s}{x} \cdot \frac{s}{x}\right)\\ \end{array} \]
Alternative 9
Error12.9
Cost452
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq 0.4000000059604645:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{x} \cdot \left(s \cdot \frac{s}{x}\right)\\ \end{array} \]
Alternative 10
Error12.4
Cost452
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq 100000:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot \left(s \cdot s\right)}{x \cdot x}\\ \end{array} \]
Alternative 11
Error16.2
Cost388
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq -1:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{2 - \frac{x}{s}}\\ \end{array} \]
Alternative 12
Error16.7
Cost356
\[\begin{array}{l} t_0 := \frac{-x}{s}\\ \mathbf{if}\;t_0 \leq 0.4000000059604645:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t_0}\\ \end{array} \]
Alternative 13
Error17.2
Cost164
\[\begin{array}{l} \mathbf{if}\;x \leq -0.20000000298023224:\\ \;\;\;\;\frac{s}{x}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \]
Alternative 14
Error21.0
Cost32
\[0.5 \]

Error

Reproduce

herbie shell --seed 2022343 
(FPCore (x s)
  :name "Logistic function"
  :precision binary32
  :pre (and (<= 0.0 s) (<= s 1.0651631))
  (/ 1.0 (+ 1.0 (exp (/ (- x) s)))))