Average Error: 17.3 → 0.0
Time: 12.9s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r401757 = x;
        double r401758 = y;
        double r401759 = r401757 * r401758;
        double r401760 = z;
        double r401761 = r401758 * r401760;
        double r401762 = r401759 - r401761;
        double r401763 = r401758 * r401758;
        double r401764 = r401762 - r401763;
        double r401765 = r401764 + r401763;
        return r401765;
}
↓
double f(double x, double y, double z) {
        double r401766 = x;
        double r401767 = z;
        double r401768 = r401766 - r401767;
        double r401769 = y;
        double r401770 = r401768 * r401769;
        return r401770;
}

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

Original17.3
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.3

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

  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, B"

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

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