Average Error: 17.4 → 0.0
Time: 20.4s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r1000587 = x;
        double r1000588 = y;
        double r1000589 = r1000587 * r1000588;
        double r1000590 = r1000588 * r1000588;
        double r1000591 = r1000589 + r1000590;
        double r1000592 = z;
        double r1000593 = r1000588 * r1000592;
        double r1000594 = r1000591 - r1000593;
        double r1000595 = r1000594 - r1000590;
        return r1000595;
}
↓
double f(double x, double y, double z) {
        double r1000596 = y;
        double r1000597 = x;
        double r1000598 = z;
        double r1000599 = r1000597 - r1000598;
        double r1000600 = r1000596 * r1000599;
        return r1000600;
}

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

Original17.4
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.4

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

  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 2019303 +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)))