Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Average Error: 0.0 → 0.0

Time: 3.6s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	18.3
Cost	724

\[\begin{array}{l} \mathbf{if}\;y \leq -5091452.155613959:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.494824283840877 \cdot 10^{-86}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.293274277846858 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6595579748351535 \cdot 10^{-20}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.00043649653100501224:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	9.7
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1228534633664728:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.00014560340274072535:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.27185687356126 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	9.5
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -9.661502896484206 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 0.00014560340274072535:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.27185687356126 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	9.3
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -9.661502896484206 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 0.00014560340274072535:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \mathbf{elif}\;y \leq 4.27185687356126 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	0.9
Cost	712

\[\begin{array}{l} t_0 := 1 + \frac{x + -1}{y}\\ \mathbf{if}\;y \leq -1.1228534633664728:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.00043649653100501224:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	9.9
Cost	588

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1228534633664728:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 123.42075535147804:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.27185687356126 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	9.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1228534633664728:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.00043649653100501224:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	35.4
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.0043370993656516 \cdot 10^{-187}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.4969648386488 \cdot 10^{-154}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	55.0
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022294 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))