Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, B

Average Error: 0.0 → 0.0

Time: 1.6s

Precision: binary64

Cost: 320

Math

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

↓

\[x + y \cdot x \]

FPCore

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

↓

(FPCore (x y) :precision binary64 (+ x (* y x)))

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

def code(x, y):
	return x + (y * x)

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.0
Target	0.0
Herbie	0.0

\[x + x \cdot y \]

Derivation

1. Initial program 0.0

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

2. Taylor expanded in y around 0 0.0

   \[\leadsto \color{blue}{y \cdot x + x} \]

3. Final simplification 0.0

   \[\leadsto x + y \cdot x \]

Alternatives

Alternative 1
Error	2.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -9.326475587132545 \cdot 10^{+19}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 7.703325917439791 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Error	26.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022317 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ x (* x y))

  (* x (+ y 1.0)))