Average Error: 13.2 → 0.0
Time: 2.4s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r465701 = x;
        double r465702 = y;
        double r465703 = r465701 * r465702;
        double r465704 = r465702 * r465702;
        double r465705 = r465703 - r465704;
        double r465706 = r465705 + r465704;
        double r465707 = z;
        double r465708 = r465702 * r465707;
        double r465709 = r465706 - r465708;
        return r465709;
}
↓
double f(double x, double y, double z) {
        double r465710 = y;
        double r465711 = x;
        double r465712 = z;
        double r465713 = r465711 - r465712;
        double r465714 = r465710 * r465713;
        return r465714;
}

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

Original13.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.2

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020039 
(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)))