Average Error: 12.9 → 0.0
Time: 2.1s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r537125 = x;
        double r537126 = y;
        double r537127 = r537125 * r537126;
        double r537128 = r537126 * r537126;
        double r537129 = r537127 - r537128;
        double r537130 = r537129 + r537128;
        double r537131 = z;
        double r537132 = r537126 * r537131;
        double r537133 = r537130 - r537132;
        return r537133;
}
↓
double f(double x, double y, double z) {
        double r537134 = y;
        double r537135 = x;
        double r537136 = z;
        double r537137 = r537135 - r537136;
        double r537138 = r537134 * r537137;
        return r537138;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

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Target

Original12.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.9

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

  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, D"
  :precision binary64

  :herbie-target
  (* (- x z) y)

  (- (+ (- (* x y) (* y y)) (* y y)) (* y z)))