Average Error: 13.3 → 0.0
Time: 2.1s
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 r619594 = x;
        double r619595 = y;
        double r619596 = r619594 * r619595;
        double r619597 = r619595 * r619595;
        double r619598 = r619596 - r619597;
        double r619599 = r619598 + r619597;
        double r619600 = z;
        double r619601 = r619595 * r619600;
        double r619602 = r619599 - r619601;
        return r619602;
}
↓
double f(double x, double y, double z) {
        double r619603 = y;
        double r619604 = x;
        double r619605 = z;
        double r619606 = r619604 - r619605;
        double r619607 = r619603 * r619606;
        return r619607;
}

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

Original13.3
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.3

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

  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 2020060 
(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)))