?

Average Error: 0.1 → 0.1
Time: 12.8s
Precision: binary32
Cost: 3456

?

\[0 \leq s \land s \leq 1.0651631\]
\[\frac{1}{1 + e^{\frac{-x}{s}}} \]
↓
\[\frac{1}{1 + e^{\frac{-x}{s}}} \]
(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)));
}

real(4) function code(x, s)
    real(4), intent (in) :: x
    real(4), intent (in) :: s
    code = 1.0e0 / (1.0e0 + exp((-x / s)))
end function
↓
real(4) function code(x, s)
    real(4), intent (in) :: x
    real(4), intent (in) :: s
    code = 1.0e0 / (1.0e0 + exp((-x / s)))
end function

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) + exp(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) + exp((-x / s)));
end

\frac{1}{1 + e^{\frac{-x}{s}}}
↓
\frac{1}{1 + e^{\frac{-x}{s}}}

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. Final simplification0.1

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

Alternatives

Alternative 1
Error12.6
Cost772
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq -10:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + \left(\left(1 - \frac{x}{s}\right) + \frac{x}{\frac{s}{x}} \cdot \frac{0.5}{s}\right)}\\ \end{array} \]
Alternative 2
Error11.6
Cost772
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq 0.019999999552965164:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + \left(\left(1 - \frac{x}{s}\right) - x \cdot \left(x \cdot \frac{\frac{-0.5}{s}}{s}\right)\right)}\\ \end{array} \]
Alternative 3
Error12.5
Cost580
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq 100:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + \frac{x \cdot \left(x \cdot 0.5\right)}{s \cdot s}}\\ \end{array} \]
Alternative 4
Error12.6
Cost452
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq 100:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{s \cdot s}{x \cdot x}\\ \end{array} \]
Alternative 5
Error16.4
Cost388
\[\begin{array}{l} \mathbf{if}\;\frac{-x}{s} \leq -10:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{2 - \frac{x}{s}}\\ \end{array} \]
Alternative 6
Error16.9
Cost356
\[\begin{array}{l} t_0 := \frac{-x}{s}\\ \mathbf{if}\;t_0 \leq 2:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t_0}\\ \end{array} \]
Alternative 7
Error17.4
Cost196
\[\begin{array}{l} \mathbf{if}\;x \leq -4.999999987376214 \cdot 10^{-7}:\\ \;\;\;\;\frac{-s}{x}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \]
Alternative 8
Error17.4
Cost164
\[\begin{array}{l} \mathbf{if}\;x \leq -0.0020000000949949026:\\ \;\;\;\;\frac{s}{x}\\ \mathbf{else}:\\ \;\;\;\;0.5\\ \end{array} \]
Alternative 9
Error20.8
Cost32
\[0.5 \]

Error

Reproduce?

herbie shell --seed 2023055 
(FPCore (x s)
  :name "Logistic function"
  :precision binary32
  :pre (and (<= 0.0 s) (<= s 1.0651631))
  (/ 1.0 (+ 1.0 (exp (/ (- x) s)))))