Average Error: 17.6 → 0.0
Time: 3.2s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r448586 = x;
        double r448587 = y;
        double r448588 = r448586 * r448587;
        double r448589 = z;
        double r448590 = r448587 * r448589;
        double r448591 = r448588 - r448590;
        double r448592 = r448587 * r448587;
        double r448593 = r448591 - r448592;
        double r448594 = r448593 + r448592;
        return r448594;
}
↓
double f(double x, double y, double z) {
        double r448595 = y;
        double r448596 = x;
        double r448597 = z;
        double r448598 = r448596 - r448597;
        double r448599 = r448595 * r448598;
        return r448599;
}

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

Original17.6
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.6

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

  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 2020039 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

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

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