Average Error: 0.0 → 0
Time: 840.0ms
Precision: 64
\[x \cdot \left(y + 1\right)\]
↓
\[\mathsf{fma}\left(y, x, x \cdot 1\right)\]
x \cdot \left(y + 1\right)
↓
\mathsf{fma}\left(y, x, x \cdot 1\right)
double code(double x, double y) {
	return (x * (y + 1.0));
}
↓
double code(double x, double y) {
	return fma(y, x, (x * 1.0));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0
\[x + x \cdot y\]

Derivation

  1. Initial program 0.0

    \[x \cdot \left(y + 1\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{x \cdot y + x \cdot 1}\]
  4. Using strategy rm

  5. Applied *-commutative0.0

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

  6. Applied fma-def0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, x \cdot 1\right)}\]

  7. Final simplification0

    \[\leadsto \mathsf{fma}\left(y, x, x \cdot 1\right)\]

Reproduce

herbie shell --seed 2020078 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ x (* x y))

  (* x (+ y 1)))