Average Error: 0.3 → 0.2
Time: 3.8s
Precision: binary64
\[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
↓
\[y \cdot \left(x \cdot \left(y \cdot 3\right)\right)\]
\left(\left(x \cdot 3\right) \cdot y\right) \cdot y
↓
y \cdot \left(x \cdot \left(y \cdot 3\right)\right)
(FPCore (x y) :precision binary64 (* (* (* x 3.0) y) y))
↓
(FPCore (x y) :precision binary64 (* y (* x (* y 3.0))))
double code(double x, double y) {
	return ((x * 3.0) * y) * y;
}
↓
double code(double x, double y) {
	return y * (x * (y * 3.0));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.2
\[\left(x \cdot \left(3 \cdot y\right)\right) \cdot y\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
  2. Using strategy rm

  3. Applied associate-*l*_binary64_143410.2

    \[\leadsto \color{blue}{\left(x \cdot \left(3 \cdot y\right)\right)} \cdot y\]

  4. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(3 \cdot \left(x \cdot y\right)\right)} \cdot y\]
  5. Using strategy rm

  6. Applied add-cube-cbrt_binary64_144350.2

    \[\leadsto \left(\color{blue}{\left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}\right)} \cdot \left(x \cdot y\right)\right) \cdot y\]

  7. Applied associate-*l*_binary64_143410.4

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\sqrt[3]{3} \cdot \left(x \cdot y\right)\right)\right)} \cdot y\]

  8. Simplified0.4

    \[\leadsto \left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot \sqrt[3]{3}\right)}\right) \cdot y\]

  9. Taylor expanded around 0 0.6

    \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot {\left(\sqrt[3]{3}\right)}^{3}\right)\right)} \cdot y\]

  10. Simplified0.2

    \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot 3\right)\right)} \cdot y\]

  11. Final simplification0.2

    \[\leadsto y \cdot \left(x \cdot \left(y \cdot 3\right)\right)\]

Reproduce

herbie shell --seed 2021075 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"
  :precision binary64

  :herbie-target
  (* (* x (* 3.0 y)) y)

  (* (* (* x 3.0) y) y))