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

Average Error: 2.1 → 2.1

Time: 18.1s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

Python

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

↓

def code(x, y, z, t):
	return ((x / y) * (z - t)) + 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(Float64(Float64(x / y) * Float64(z - t)) + 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 = ((x / y) * (z - t)) + 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[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Target

Original	2.1
Target	2.3
Herbie	2.1

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

Derivation

1. Initial program 2.1

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

2. Final simplification 2.1

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

Alternatives

Alternative 1
Error	27.1
Cost	1572

\[\begin{array}{l} t_1 := \frac{z}{y} \cdot x\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{-74}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-143}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-209}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-258}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-79}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-47}:\\ \;\;\;\;-\frac{t \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 2
Error	27.2
Cost	1572

\[\begin{array}{l} t_1 := \frac{z}{y} \cdot x\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{-76}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-142}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-208}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-258}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-78}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-47}:\\ \;\;\;\;\left(-\frac{t}{y}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3
Error	15.3
Cost	1488

\[\begin{array}{l} t_1 := \frac{z - t}{y} \cdot x\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-184}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	26.8
Cost	1244

\[\begin{array}{l} t_1 := \frac{z}{y} \cdot x\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{-75}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-143}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-209}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-258}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5
Error	18.1
Cost	1108

\[\begin{array}{l} t_1 := \frac{z}{y} \cdot x\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{-142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-212}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-258}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	6.4
Cost	968

\[\begin{array}{l} t_1 := \frac{z - t}{y} \cdot x\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.002:\\ \;\;\;\;\frac{z \cdot x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	6.0
Cost	968

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.002:\\ \;\;\;\;\frac{z \cdot x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \end{array} \]

Alternative 8
Error	26.3
Cost	848

\[\begin{array}{l} t_1 := \frac{z}{y} \cdot x\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{-76}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-143}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9
Error	32.0
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023088 
(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))