Average Error: 13.2 → 0.0
Time: 1.3s
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 r447664 = x;
        double r447665 = y;
        double r447666 = r447664 * r447665;
        double r447667 = r447665 * r447665;
        double r447668 = r447666 - r447667;
        double r447669 = r447668 + r447667;
        double r447670 = z;
        double r447671 = r447665 * r447670;
        double r447672 = r447669 - r447671;
        return r447672;
}
↓
double f(double x, double y, double z) {
        double r447673 = y;
        double r447674 = x;
        double r447675 = z;
        double r447676 = r447674 - r447675;
        double r447677 = r447673 * r447676;
        return r447677;
}

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

Original13.2
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 2020064 +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)))