Average Error: 17.5 → 0.0
Time: 2.0s
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 r698819 = x;
        double r698820 = y;
        double r698821 = r698819 * r698820;
        double r698822 = z;
        double r698823 = r698820 * r698822;
        double r698824 = r698821 - r698823;
        double r698825 = r698820 * r698820;
        double r698826 = r698824 - r698825;
        double r698827 = r698826 + r698825;
        return r698827;
}
↓
double f(double x, double y, double z) {
        double r698828 = y;
        double r698829 = x;
        double r698830 = z;
        double r698831 = r698829 - r698830;
        double r698832 = r698828 * r698831;
        return r698832;
}

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

Original17.5
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.5

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

  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 2020025 
(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)))