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 r570368 = x;
        double r570369 = y;
        double r570370 = r570368 * r570369;
        double r570371 = r570369 * r570369;
        double r570372 = r570370 - r570371;
        double r570373 = r570372 + r570371;
        double r570374 = z;
        double r570375 = r570369 * r570374;
        double r570376 = r570373 - r570375;
        return r570376;
}
↓
double f(double x, double y, double z) {
        double r570377 = y;
        double r570378 = x;
        double r570379 = z;
        double r570380 = r570378 - r570379;
        double r570381 = r570377 * r570380;
        return r570381;
}

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 2020027 
(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)))