Average Error: 12.9 → 0.0
Time: 17.6s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r444223 = x;
        double r444224 = y;
        double r444225 = r444223 * r444224;
        double r444226 = r444224 * r444224;
        double r444227 = r444225 - r444226;
        double r444228 = r444227 + r444226;
        double r444229 = z;
        double r444230 = r444224 * r444229;
        double r444231 = r444228 - r444230;
        return r444231;
}
↓
double f(double x, double y, double z) {
        double r444232 = x;
        double r444233 = z;
        double r444234 = r444232 - r444233;
        double r444235 = y;
        double r444236 = r444234 * r444235;
        return r444236;
}

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

    \[\leadsto \color{blue}{\left(x - z\right) \cdot y}\]

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(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)))