Average Error: 12.9 → 0.0
Time: 12.2s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r792488 = x;
        double r792489 = y;
        double r792490 = r792488 * r792489;
        double r792491 = r792489 * r792489;
        double r792492 = r792490 - r792491;
        double r792493 = r792492 + r792491;
        double r792494 = z;
        double r792495 = r792489 * r792494;
        double r792496 = r792493 - r792495;
        return r792496;
}
↓
double f(double x, double y, double z) {
        double r792497 = x;
        double r792498 = z;
        double r792499 = r792497 - r792498;
        double r792500 = y;
        double r792501 = r792499 * r792500;
        return r792501;
}

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

Original12.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.9

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64

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

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