Average Error: 12.8 → 0.0
Time: 20.7s
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 r339992 = x;
        double r339993 = y;
        double r339994 = r339992 * r339993;
        double r339995 = r339993 * r339993;
        double r339996 = r339994 - r339995;
        double r339997 = r339996 + r339995;
        double r339998 = z;
        double r339999 = r339993 * r339998;
        double r340000 = r339997 - r339999;
        return r340000;
}
↓
double f(double x, double y, double z) {
        double r340001 = y;
        double r340002 = x;
        double r340003 = z;
        double r340004 = r340002 - r340003;
        double r340005 = r340001 * r340004;
        return r340005;
}

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

Original12.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.8

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

  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 2019209 +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)))