Average Error: 17.4 → 0.0
Time: 20.2s
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 r402755 = x;
        double r402756 = y;
        double r402757 = r402755 * r402756;
        double r402758 = r402756 * r402756;
        double r402759 = r402757 + r402758;
        double r402760 = z;
        double r402761 = r402756 * r402760;
        double r402762 = r402759 - r402761;
        double r402763 = r402762 - r402758;
        return r402763;
}
↓
double f(double x, double y, double z) {
        double r402764 = y;
        double r402765 = x;
        double r402766 = z;
        double r402767 = r402765 - r402766;
        double r402768 = r402764 * r402767;
        return r402768;
}

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)))