Average Error: 17.9 → 0.0
Time: 10.4s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r623521 = x;
        double r623522 = y;
        double r623523 = r623521 * r623522;
        double r623524 = r623522 * r623522;
        double r623525 = r623523 + r623524;
        double r623526 = z;
        double r623527 = r623522 * r623526;
        double r623528 = r623525 - r623527;
        double r623529 = r623528 - r623524;
        return r623529;
}
↓
double f(double x, double y, double z) {
        double r623530 = x;
        double r623531 = z;
        double r623532 = r623530 - r623531;
        double r623533 = y;
        double r623534 = r623532 * r623533;
        return r623534;
}

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

Original17.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.9

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(x - z\right) \cdot y}\]

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

  :herbie-target
  (* (- x z) y)

  (- (- (+ (* x y) (* y y)) (* y z)) (* y y)))