Average Error: 17.2 → 0.0
Time: 10.4s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r639133 = x;
        double r639134 = y;
        double r639135 = r639133 * r639134;
        double r639136 = z;
        double r639137 = r639134 * r639136;
        double r639138 = r639135 - r639137;
        double r639139 = r639134 * r639134;
        double r639140 = r639138 - r639139;
        double r639141 = r639140 + r639139;
        return r639141;
}
↓
double f(double x, double y, double z) {
        double r639142 = y;
        double r639143 = x;
        double r639144 = z;
        double r639145 = r639143 - r639144;
        double r639146 = r639142 * r639145;
        return r639146;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

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Target

Original17.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.2

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

  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 2020047 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

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

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