Average Error: 0.0 → 0.0
Time: 1.1s
Precision: binary64
Cost: 320
\[x \cdot \left(y + 1\right)\]
↓
\[x + x \cdot y\]
x \cdot \left(y + 1\right)
↓
x + x \cdot y
(FPCore (x y) :precision binary64 (* x (+ y 1.0)))
↓
(FPCore (x y) :precision binary64 (+ x (* x y)))
double code(double x, double y) {
	return x * (y + 1.0);
}
↓
double code(double x, double y) {
	return x + (x * y);
}

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

Alternatives

Alternative 1
Error1.6
Cost520
\[\begin{array}{l} \mathbf{if}\;y \leq -1.0003264447769855 \lor \neg \left(y \leq 0.9928595778330866\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
Alternative 2
Error27.1
Cost64
\[x\]
Alternative 3
Error61.8
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

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

  3. Applied distribute-rgt-in_binary64_170780.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

    \[\leadsto x + x \cdot y\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, B"
  :precision binary64

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

  (* x (+ y 1.0)))