?

Average Error: 0.1 → 0.1
Time: 9.2s
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

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

  3. Final simplification0.1

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

Alternatives

Alternative 1
Error0.8
Cost3556
\[\begin{array}{l} t_0 := \frac{-x}{s}\\ \mathbf{if}\;t_0 \leq -3:\\ \;\;\;\;1 + e^{t_0}\\ \mathbf{elif}\;t_0 \leq 1:\\ \;\;\;\;0.5 + x \cdot \frac{0.25}{s}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
Alternative 2
Error0.1
Cost3456
\[\frac{1}{1 + e^{\frac{-x}{s}}} \]
Alternative 3
Error10.0
Cost196
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq 20:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
Alternative 4
Error20.6
Cost32
\[0.5 \]

Error

Reproduce?

herbie shell --seed 2023187 
(FPCore (x s)
  :name "Logistic function"
  :precision binary32
  :pre (and (<= 0.0 s) (<= s 1.0651631))
  (/ 1.0 (+ 1.0 (exp (/ (- x) s)))))