Average Error: 17.1 → 0.0
Time: 1.5s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r519483 = x;
        double r519484 = y;
        double r519485 = r519483 * r519484;
        double r519486 = z;
        double r519487 = r519484 * r519486;
        double r519488 = r519485 - r519487;
        double r519489 = r519484 * r519484;
        double r519490 = r519488 - r519489;
        double r519491 = r519490 + r519489;
        return r519491;
}
↓
double f(double x, double y, double z) {
        double r519492 = y;
        double r519493 = x;
        double r519494 = z;
        double r519495 = r519493 - r519494;
        double r519496 = r519492 * r519495;
        return r519496;
}

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

Original17.1
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.1

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019356 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

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

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