Average Error: 0.3 → 0.2
Time: 1.6s
Precision: binary64
\[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y \]
↓
\[y \cdot \left(3 \cdot \left(y \cdot x\right)\right) \]
\left(\left(x \cdot 3\right) \cdot y\right) \cdot y
↓
y \cdot \left(3 \cdot \left(y \cdot x\right)\right)

(FPCore (x y) :precision binary64 (* (* (* x 3.0) y) y))
↓
(FPCore (x y) :precision binary64 (* y (* 3.0 (* y x))))
double code(double x, double y) {
	return ((x * 3.0) * y) * y;
}
↓
double code(double x, double y) {
	return y * (3.0 * (y * x));
}

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. Applied associate-*l*_binary640.2

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

  3. Applied *-un-lft-identity_binary640.2

    \[\leadsto \left(\color{blue}{\left(1 \cdot x\right)} \cdot \left(3 \cdot y\right)\right) \cdot y \]

  4. Applied associate-*l*_binary640.2

    \[\leadsto \color{blue}{\left(1 \cdot \left(x \cdot \left(3 \cdot y\right)\right)\right)} \cdot y \]

  5. Simplified0.2

    \[\leadsto \left(1 \cdot \color{blue}{\left(3 \cdot \left(y \cdot x\right)\right)}\right) \cdot y \]

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2022077 
(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))