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

Average Accuracy: 96.8% → 96.8%

Time: 12.4s

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	96.8%
Target	96.7%
Herbie	96.8%

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

Derivation

1. Initial program 96.8%

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

2. Final simplification 96.8%

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

Alternatives

Alternative 1
Accuracy	74.9%
Cost	1636

\[\begin{array}{l} t_1 := \frac{t}{\frac{z - y}{x}}\\ t_2 := \frac{t}{\frac{z}{x - y}}\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-229}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-21}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.05:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 2
Accuracy	75.3%
Cost	1372

\[\begin{array}{l} t_1 := \frac{t}{\frac{z - y}{x}}\\ t_2 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{-28}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-306}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-221}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-219}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-178}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 64000000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	74.7%
Cost	976

\[\begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-25}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 230:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	74.8%
Cost	976

\[\begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-20}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 580:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 56000000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 5
Accuracy	84.7%
Cost	973

\[\begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+217}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-69} \lor \neg \left(x \leq 2.2 \cdot 10^{-113}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]

Alternative 6
Accuracy	70.7%
Cost	844

\[\begin{array}{l} t_1 := \frac{t}{\frac{z}{x - y}}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-190}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+50}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	59.1%
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-89}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-26}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Accuracy	67.9%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-89} \lor \neg \left(y \leq 2.8 \cdot 10^{-29}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \end{array} \]

Alternative 9
Accuracy	69.4%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+104} \lor \neg \left(z \leq 1.15 \cdot 10^{+50}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 10
Accuracy	60.1%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-13}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11
Accuracy	60.0%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12
Accuracy	37.7%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023138 
(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))