Average Error: 12.6 → 0.0
Time: 12.6s
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 r477457 = x;
        double r477458 = y;
        double r477459 = r477457 * r477458;
        double r477460 = r477458 * r477458;
        double r477461 = r477459 - r477460;
        double r477462 = r477461 + r477460;
        double r477463 = z;
        double r477464 = r477458 * r477463;
        double r477465 = r477462 - r477464;
        return r477465;
}
↓
double f(double x, double y, double z) {
        double r477466 = x;
        double r477467 = z;
        double r477468 = r477466 - r477467;
        double r477469 = y;
        double r477470 = r477468 * r477469;
        return r477470;
}

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

Original12.6
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.6

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"

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

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