Average Error: 17.5 → 0.0
Time: 2.1s
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 r683162 = x;
        double r683163 = y;
        double r683164 = r683162 * r683163;
        double r683165 = z;
        double r683166 = r683163 * r683165;
        double r683167 = r683164 - r683166;
        double r683168 = r683163 * r683163;
        double r683169 = r683167 - r683168;
        double r683170 = r683169 + r683168;
        return r683170;
}
↓
double f(double x, double y, double z) {
        double r683171 = y;
        double r683172 = x;
        double r683173 = z;
        double r683174 = r683172 - r683173;
        double r683175 = r683171 * r683174;
        return r683175;
}

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 2020100 +o rules:numerics
(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)))