Average Error: 13.3 → 0.0
Time: 3.5s
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 r472653 = x;
        double r472654 = y;
        double r472655 = r472653 * r472654;
        double r472656 = r472654 * r472654;
        double r472657 = r472655 - r472656;
        double r472658 = r472657 + r472656;
        double r472659 = z;
        double r472660 = r472654 * r472659;
        double r472661 = r472658 - r472660;
        return r472661;
}
↓
double f(double x, double y, double z) {
        double r472662 = y;
        double r472663 = x;
        double r472664 = z;
        double r472665 = r472663 - r472664;
        double r472666 = r472662 * r472665;
        return r472666;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original13.3
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.3

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

  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 2020036 +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)))