Average Error: 0.1 → 0.1
Time: 13.8s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[z \cdot \left(z \cdot 3\right) + x \cdot y\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
z \cdot \left(z \cdot 3\right) + x \cdot y
double f(double x, double y, double z) {
        double r24707038 = x;
        double r24707039 = y;
        double r24707040 = r24707038 * r24707039;
        double r24707041 = z;
        double r24707042 = r24707041 * r24707041;
        double r24707043 = r24707040 + r24707042;
        double r24707044 = r24707043 + r24707042;
        double r24707045 = r24707044 + r24707042;
        return r24707045;
}
↓
double f(double x, double y, double z) {
        double r24707046 = z;
        double r24707047 = 3.0;
        double r24707048 = r24707046 * r24707047;
        double r24707049 = r24707046 * r24707048;
        double r24707050 = x;
        double r24707051 = y;
        double r24707052 = r24707050 * r24707051;
        double r24707053 = r24707049 + r24707052;
        return r24707053;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Target

Original0.1
Target0.1
Herbie0.1
\[\left(3 \cdot z\right) \cdot z + y \cdot x\]

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

    \[\leadsto \color{blue}{\left(z \cdot z\right) \cdot 3 + x \cdot y}\]
  3. Using strategy rm

  4. Applied associate-*l*0.1

    \[\leadsto \color{blue}{z \cdot \left(z \cdot 3\right)} + x \cdot y\]

  5. Final simplification0.1

    \[\leadsto z \cdot \left(z \cdot 3\right) + x \cdot y\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"

  :herbie-target
  (+ (* (* 3 z) z) (* y x))

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