Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3

Average Error: 0.0 → 0.0

Time: 2.2s

Precision: binary64

Cost: 576

Math

\[x \cdot y + \left(1 - x\right) \cdot z \]

↓

\[\left(1 - x\right) \cdot z + x \cdot y \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* (- 1.0 x) z)))

↓

(FPCore (x y z) :precision binary64 (+ (* (- 1.0 x) z) (* x y)))

C

double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}

↓

double code(double x, double y, double z) {
	return ((1.0 - x) * z) + (x * y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * y) + ((1.0d0 - x) * z)
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((1.0d0 - x) * z) + (x * y)
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}

↓

public static double code(double x, double y, double z) {
	return ((1.0 - x) * z) + (x * y);
}

Python

def code(x, y, z):
	return (x * y) + ((1.0 - x) * z)

↓

def code(x, y, z):
	return ((1.0 - x) * z) + (x * y)

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(Float64(1.0 - x) * z))
end

↓

function code(x, y, z)
	return Float64(Float64(Float64(1.0 - x) * z) + Float64(x * y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + ((1.0 - x) * z);
end

↓

function tmp = code(x, y, z)
	tmp = ((1.0 - x) * z) + (x * y);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[x \cdot y + \left(1 - x\right) \cdot z \]

2. Final simplification 0.0

   \[\leadsto \left(1 - x\right) \cdot z + x \cdot y \]

Alternatives

Alternative 1
Error	14.8
Cost	848

\[\begin{array}{l} t_0 := z - x \cdot z\\ t_1 := x \cdot \left(y - z\right)\\ \mathbf{if}\;z \leq -6.68337000111986 \cdot 10^{+21}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.2257532009159281 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.63350159373066 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.2580619758485436 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	26.0
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -6.68337000111986 \cdot 10^{+21}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.2257532009159281 \cdot 10^{-96}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 2.63350159373066 \cdot 10^{-11}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.2580619758485436 \cdot 10^{+85}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 3
Error	24.8
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+96}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -117400125672067660:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -4.885592608485508 \cdot 10^{-129}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.0837309768533918 \cdot 10^{-15}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4
Error	16.1
Cost	584

\[\begin{array}{l} t_0 := z - x \cdot z\\ \mathbf{if}\;z \leq -9.415968692039606 \cdot 10^{-97}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.2257532009159281 \cdot 10^{-96}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	35.1
Cost	64

\[z \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))