Average Error: 12.9 → 0.0
Time: 1.8s
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 r485654 = x;
        double r485655 = y;
        double r485656 = r485654 * r485655;
        double r485657 = r485655 * r485655;
        double r485658 = r485656 - r485657;
        double r485659 = r485658 + r485657;
        double r485660 = z;
        double r485661 = r485655 * r485660;
        double r485662 = r485659 - r485661;
        return r485662;
}
↓
double f(double x, double y, double z) {
        double r485663 = y;
        double r485664 = x;
        double r485665 = z;
        double r485666 = r485664 - r485665;
        double r485667 = r485663 * r485666;
        return r485667;
}

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

Original12.9
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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(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)))