Average Error: 0.1 → 0.1
Time: 2.9s
Precision: binary64
\[x \cdot \left(y + z\right) + z \cdot 5\]
↓
\[\left(x \cdot y + x \cdot z\right) + z \cdot 5\]
x \cdot \left(y + z\right) + z \cdot 5
↓
\left(x \cdot y + x \cdot z\right) + z \cdot 5
(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))
↓
(FPCore (x y z) :precision binary64 (+ (+ (* x y) (* x z)) (* z 5.0)))
double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}
↓
double code(double x, double y, double z) {
	return ((x * y) + (x * z)) + (z * 5.0);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\left(x + 5\right) \cdot z + x \cdot y\]

Derivation

  1. Initial program 0.1

    \[x \cdot \left(y + z\right) + z \cdot 5\]
  2. Using strategy rm

  3. Applied distribute-rgt-in_binary640.1

    \[\leadsto \color{blue}{\left(y \cdot x + z \cdot x\right)} + z \cdot 5\]

  4. Simplified0.1

    \[\leadsto \left(\color{blue}{x \cdot y} + z \cdot x\right) + z \cdot 5\]

  5. Simplified0.1

    \[\leadsto \left(x \cdot y + \color{blue}{x \cdot z}\right) + z \cdot 5\]

  6. Final simplification0.1

    \[\leadsto \left(x \cdot y + x \cdot z\right) + z \cdot 5\]

Reproduce

herbie shell --seed 2020233 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :herbie-target
  (+ (* (+ x 5.0) z) (* x y))

  (+ (* x (+ y z)) (* z 5.0)))