Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 1.7s

Precision: binary64

Cost: 6720

Math

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

↓

\[\mathsf{fma}\left(x, y, y\right) - x \]

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 100.0%

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

2. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, y\right) - x} \]

3. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, y, y\right) - x \]

Alternatives

Alternative 1
Accuracy	98.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1.5 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 2
Accuracy	61.2%
Cost	456

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

Alternative 3
Accuracy	75.8%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+210}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+113}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4
Accuracy	100.0%
Cost	448

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

Alternative 5
Accuracy	38.6%
Cost	128

\[-x \]

Reproduce

herbie shell --seed 2023161 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))