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

Average Error: 2.3 → 2.3

Time: 13.8s

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	2.3
Target	2.3
Herbie	2.3

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

Derivation

1. Initial program 2.3

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

2. Final simplification 2.3

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

Alternatives

Alternative 1
Error	25.9
Cost	1372

\[\begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+151}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-37}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-25}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 3100000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+96}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	19.2
Cost	1240

\[\begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{t}{y}\\ t_2 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{-25}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 5200000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	19.3
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{+33}:\\ \;\;\;\;t - \frac{x}{\frac{y}{t}}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 2900000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	19.2
Cost	1240

\[\begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;t - \frac{x}{\frac{y}{t}}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-24}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 5500000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	16.6
Cost	1240

\[\begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ t_2 := \frac{t}{\frac{z}{x - y}}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+34}:\\ \;\;\;\;t - \frac{x}{\frac{y}{t}}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5600000000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	16.7
Cost	1240

\[\begin{array}{l} t_1 := \frac{t}{\frac{z}{x - y}}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+57}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+34}:\\ \;\;\;\;t - \frac{x}{\frac{y}{t}}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 13500000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \]

Alternative 7
Error	16.8
Cost	1240

\[\begin{array}{l} t_1 := \frac{t}{\frac{z - y}{x}}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-25}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 1150000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \]

Alternative 8
Error	25.1
Cost	980

\[\begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-37}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 10^{+56}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9
Error	25.0
Cost	980

\[\begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+84}:\\ \;\;\;\;\frac{-t}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-36}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10
Error	25.1
Cost	980

\[\begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+115}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+84}:\\ \;\;\;\;\frac{-t}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+62}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11
Error	25.6
Cost	980

\[\begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+114}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+57}:\\ \;\;\;\;\frac{-t}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+56}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12
Error	25.5
Cost	980

\[\begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+55}:\\ \;\;\;\;\frac{-t}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+55}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13
Error	25.5
Cost	980

\[\begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+57}:\\ \;\;\;\;\frac{-t}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+16}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{elif}\;y \leq -7.1 \cdot 10^{-37}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+55}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14
Error	7.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+151}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+241}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]

Alternative 15
Error	25.5
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16
Error	24.5
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17
Error	24.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18
Error	39.3
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023039 
(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))