Data.Colour.RGB:hslsv from colour-2.3.3, E

Average Error: 0.0 → 0.0

Time: 2.3s

Precision: binary64

Cost: 320

Math

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

↓

\[1 - \frac{y}{x} \]

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.0
Target	0.0
Herbie	0.0

\[1 - \frac{y}{x} \]

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

   \[\leadsto \color{blue}{1 - \frac{y}{x}} \]
   Proof
   (-.f64 1 (/.f64 y x)): 0 points increase in error, 0 points decrease in error
   (-.f64 (Rewrite<= *-inverses_binary64 (/.f64 x x)) (/.f64 y x)): 0 points increase in error, 0 points decrease in error
   (Rewrite<= div-sub_binary64 (/.f64 (-.f64 x y) x)): 4 points increase in error, 1 points decrease in error

3. Final simplification 0.0

   \[\leadsto 1 - \frac{y}{x} \]

Alternatives

Alternative 1
Error	19.0
Cost	784

\[\begin{array}{l} t_0 := \frac{-y}{x}\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{-113}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.14198742348163 \cdot 10^{-57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.786840695533949 \cdot 10^{-27}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.230713039378408 \cdot 10^{+62}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	27.3
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022298 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- 1.0 (/ y x))

  (/ (- x y) x))