Average Error: 17.9 → 0.0
Time: 8.8s
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 r649121 = x;
        double r649122 = y;
        double r649123 = r649121 * r649122;
        double r649124 = r649122 * r649122;
        double r649125 = r649123 + r649124;
        double r649126 = z;
        double r649127 = r649122 * r649126;
        double r649128 = r649125 - r649127;
        double r649129 = r649128 - r649124;
        return r649129;
}
↓
double f(double x, double y, double z) {
        double r649130 = y;
        double r649131 = x;
        double r649132 = z;
        double r649133 = r649131 - r649132;
        double r649134 = r649130 * r649133;
        return r649134;
}

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

Original17.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.9

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

  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 2020046 
(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)))