Average Error: 12.9 → 0.0
Time: 2.0s
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 r419220 = x;
        double r419221 = y;
        double r419222 = r419220 * r419221;
        double r419223 = r419221 * r419221;
        double r419224 = r419222 - r419223;
        double r419225 = r419224 + r419223;
        double r419226 = z;
        double r419227 = r419221 * r419226;
        double r419228 = r419225 - r419227;
        return r419228;
}
↓
double f(double x, double y, double z) {
        double r419229 = y;
        double r419230 = x;
        double r419231 = z;
        double r419232 = r419230 - r419231;
        double r419233 = r419229 * r419232;
        return r419233;
}

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

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 2020100 +o rules:numerics
(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)))