Average Error: 17.8 → 0.0
Time: 1.9s
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 r479654 = x;
        double r479655 = y;
        double r479656 = r479654 * r479655;
        double r479657 = r479655 * r479655;
        double r479658 = r479656 + r479657;
        double r479659 = z;
        double r479660 = r479655 * r479659;
        double r479661 = r479658 - r479660;
        double r479662 = r479661 - r479657;
        return r479662;
}
↓
double f(double x, double y, double z) {
        double r479663 = y;
        double r479664 = x;
        double r479665 = z;
        double r479666 = r479664 - r479665;
        double r479667 = r479663 * r479666;
        return r479667;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

Enter valid numbers for all inputs

Target

Original17.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.8

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

  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 2020062 
(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)))