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

Average Error: 0.0 → 0.0

Time: 11.0s

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. Taylor expanded in x around 0 0.0

   \[\leadsto \color{blue}{1 + -1 \cdot \frac{y}{x}} \]

3. Simplified 0.0

   \[\leadsto \color{blue}{1 - \frac{y}{x}} \]
   Proof

   [Start] 0.0	\[ 1 + -1 \cdot \frac{y}{x} \]
   rational.json-simplify-17 [=>] 0.0	\[ \color{blue}{-1 \cdot \frac{y}{x} - -1} \]
   rational.json-simplify-2 [=>] 0.0	\[ \color{blue}{\frac{y}{x} \cdot -1} - -1 \]
   rational.json-simplify-9 [=>] 0.0	\[ \color{blue}{\left(-\frac{y}{x}\right)} - -1 \]
   rational.json-simplify-12 [=>] 0.0	\[ \color{blue}{\left(0 - \frac{y}{x}\right)} - -1 \]
   rational.json-simplify-42 [=>] 0.0	\[ \color{blue}{\left(0 - -1\right) - \frac{y}{x}} \]
   metadata-eval [=>] 0.0	\[ \color{blue}{1} - \frac{y}{x} \]

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	20.2
Cost	1312

\[\begin{array}{l} t_0 := -\frac{y}{x}\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+54}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-193}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-168}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-73}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-51}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	27.1
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023068 
(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))