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

Average Accuracy: 96.8% → 96.8%

Time: 10.9s

Precision: binary64

Cost: 576

Math

\[\frac{x}{y} \cdot \left(z - t\right) + t \]

↓

\[t + \frac{x}{y} \cdot \left(z - t\right) \]

FPCore

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

↓

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

C

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

↓

double code(double x, double y, double z, double t) {
	return t + ((x / y) * (z - 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 - t)) + 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 = t + ((x / y) * (z - t))
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	96.8%
Target	96.3%
Herbie	96.8%

\[\begin{array}{l} \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array} \]

Derivation

1. Initial program 96.8%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]

2. Final simplification 96.8%

   \[\leadsto t + \frac{x}{y} \cdot \left(z - t\right) \]

Alternatives

Alternative 1
Accuracy	64.2%
Cost	2205

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot \left(-t\right)\\ t_2 := \frac{x}{y} \cdot z\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+200}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-98}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 6 \cdot 10^{+88} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+127}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Accuracy	64.5%
Cost	2204

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot \left(-t\right)\\ t_2 := \frac{x}{y} \cdot z\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+200}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-98}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 6 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \end{array} \]

Alternative 3
Accuracy	77.3%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-55} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-27}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4
Accuracy	88.7%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-46} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \end{array} \]

Alternative 5
Accuracy	87.9%
Cost	968

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-27}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]

Alternative 6
Accuracy	87.9%
Cost	968

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \left(\frac{z}{y} - \frac{t}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-27}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]

Alternative 7
Accuracy	63.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-55} \lor \neg \left(\frac{x}{y} \leq 10^{-98}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Accuracy	63.8%
Cost	840

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-98}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 9
Accuracy	50.7%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023130 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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