Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Average Error: 2.1 → 2.1

Time: 20.8s

Precision: binary64

Cost: 576

Math

\[\frac{x - y}{z - y} \cdot t \]

↓

\[\frac{x - y}{z - y} \cdot t \]

FPCore

(FPCore (x y z t) :precision binary64 (* (/ (- x y) (- z y)) t))

↓

(FPCore (x y z t) :precision binary64 (* (/ (- x y) (- z y)) t))

C

double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}

↓

double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x - y) / (z - y)) * t
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x - y) / (z - y)) * t
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}

↓

public static double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}

Python

def code(x, y, z, t):
	return ((x - y) / (z - y)) * t

↓

def code(x, y, z, t):
	return ((x - y) / (z - y)) * t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x - y) / Float64(z - y)) * t)
end

↓

function code(x, y, z, t)
	return Float64(Float64(Float64(x - y) / Float64(z - y)) * t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x - y) / (z - y)) * t;
end

↓

function tmp = code(x, y, z, t)
	tmp = ((x - y) / (z - y)) * t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]

↓

code[x_, y_, z_, t_] := N[(N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]

Target

Original	2.1
Target	2.1
Herbie	2.1

\[\frac{t}{\frac{z - y}{x - y}} \]

Derivation

1. Initial program 2.1

   \[\frac{x - y}{z - y} \cdot t \]

Alternatives

Alternative 1
Error	19.5
Cost	1504

\[\begin{array}{l} t_1 := \frac{-y \cdot t}{z - y}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ t_3 := \frac{x - y}{z} \cdot t\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+199}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+127}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-74}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;z \leq 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	17.7
Cost	976

\[\begin{array}{l} t_1 := \frac{t}{z} \cdot \left(x - y\right)\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	6.8
Cost	840

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+175}:\\ \;\;\;\;\frac{t}{z - y} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	16.6
Cost	776

\[\begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+27}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{x}{y}\right) + t\\ \end{array} \]

Alternative 5
Error	19.8
Cost	712

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.46 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	16.6
Cost	712

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+28}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	25.7
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Error	24.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9
Error	39.6
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

  (* (/ (- x y) (- z y)) t))