Average Error: 17.6 → 0.0
Time: 2.5s
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 r473806 = x;
        double r473807 = y;
        double r473808 = r473806 * r473807;
        double r473809 = z;
        double r473810 = r473807 * r473809;
        double r473811 = r473808 - r473810;
        double r473812 = r473807 * r473807;
        double r473813 = r473811 - r473812;
        double r473814 = r473813 + r473812;
        return r473814;
}
↓
double f(double x, double y, double z) {
        double r473815 = y;
        double r473816 = x;
        double r473817 = z;
        double r473818 = r473816 - r473817;
        double r473819 = r473815 * r473818;
        return r473819;
}

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 2020036 
(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)))