Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H

Average Error: 0.0 → 0.0

Time: 1.5s

Precision: binary64

Cost: 320

Math

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

↓

\[x - x \cdot y \]

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

   \[\leadsto \color{blue}{x - x \cdot y} \]
   Proof
   (-.f64 x (*.f64 x y)): 0 points increase in error, 0 points decrease in error
   (-.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 x 1)) (*.f64 x y)): 0 points increase in error, 0 points decrease in error
   (Rewrite=> distribute-lft-out--_binary64 (*.f64 x (-.f64 1 y))): 1 points increase in error, 1 points decrease in error

3. Final simplification 0.0

   \[\leadsto x - x \cdot y \]

Alternatives

Alternative 1
Error	1.9
Cost	520

\[\begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -206612452.3914657:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.1138884767877712 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	28.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022295 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H"
  :precision binary64
  (* x (- 1.0 y)))