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

Average Error: 0.0 → 0

Time: 1.6s

Precision: binary64

Cost: 6656

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Simplified 0

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, -y, x\right)} \]
   Proof
   (fma.f64 x (neg.f64 y) x): 0 points increase in error, 0 points decrease in error
   (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (neg.f64 y)) x)): 0 points increase in error, 0 points decrease in error
   (+.f64 (*.f64 x (neg.f64 y)) (Rewrite<= *-rgt-identity_binary64 (*.f64 x 1))): 0 points increase in error, 0 points decrease in error
   (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 x 1) (*.f64 x (neg.f64 y)))): 0 points increase in error, 0 points decrease in error
   (Rewrite<= distribute-lft-in_binary64 (*.f64 x (+.f64 1 (neg.f64 y)))): 0 points increase in error, 0 points decrease in error
   (*.f64 x (Rewrite<= sub-neg_binary64 (-.f64 1 y))): 0 points increase in error, 0 points decrease in error

3. Final simplification 0

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

Alternatives

Alternative 1
Error	1.6
Cost	521

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

Alternative 2
Error	0.0
Cost	320

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

Alternative 3
Error	0.0
Cost	320

\[x - x \cdot y \]

Alternative 4
Error	27.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022349 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H"
  :precision binary64
  (* x (- 1.0 y)))