Average Error: 12.4 → 0.0
Time: 7.9s
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 r558286 = x;
        double r558287 = y;
        double r558288 = r558286 * r558287;
        double r558289 = r558287 * r558287;
        double r558290 = r558288 - r558289;
        double r558291 = r558290 + r558289;
        double r558292 = z;
        double r558293 = r558287 * r558292;
        double r558294 = r558291 - r558293;
        return r558294;
}
↓
double f(double x, double y, double z) {
        double r558295 = y;
        double r558296 = x;
        double r558297 = z;
        double r558298 = r558296 - r558297;
        double r558299 = r558295 * r558298;
        return r558299;
}

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

Original12.4
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.4

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

  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 2020047 +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)))