Average Error: 0.1 → 0.1
Time: 2.5s
Precision: binary64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[z \cdot z + \left(z \cdot z + \left(x \cdot y + z \cdot z\right)\right)\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
z \cdot z + \left(z \cdot z + \left(x \cdot y + z \cdot z\right)\right)
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (((double) (x * y)) + ((double) (z * z)))) + ((double) (z * z)))) + ((double) (z * z))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (z * z)) + ((double) (((double) (z * z)) + ((double) (((double) (x * y)) + ((double) (z * z))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\left(3 \cdot z\right) \cdot z + y \cdot x\]

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2020196 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"
  :precision binary64

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

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