Average Error: 0.2 → 0.1
Time: 2.7s
Precision: 64
\[\left(x \cdot 3\right) \cdot y - z\]
↓
\[{\left(3 \cdot \left(x \cdot y\right)\right)}^{1} - z\]
\left(x \cdot 3\right) \cdot y - z
↓
{\left(3 \cdot \left(x \cdot y\right)\right)}^{1} - z
double f(double x, double y, double z) {
        double r696564 = x;
        double r696565 = 3.0;
        double r696566 = r696564 * r696565;
        double r696567 = y;
        double r696568 = r696566 * r696567;
        double r696569 = z;
        double r696570 = r696568 - r696569;
        return r696570;
}
↓
double f(double x, double y, double z) {
        double r696571 = 3.0;
        double r696572 = x;
        double r696573 = y;
        double r696574 = r696572 * r696573;
        double r696575 = r696571 * r696574;
        double r696576 = 1.0;
        double r696577 = pow(r696575, r696576);
        double r696578 = z;
        double r696579 = r696577 - r696578;
        return r696579;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Target

Original0.2
Target0.2
Herbie0.1
\[x \cdot \left(3 \cdot y\right) - z\]

Derivation

  1. Initial program 0.2

    \[\left(x \cdot 3\right) \cdot y - z\]
  2. Using strategy rm

  3. Applied pow10.2

    \[\leadsto \left(x \cdot 3\right) \cdot \color{blue}{{y}^{1}} - z\]

  4. Applied pow10.2

    \[\leadsto \left(x \cdot \color{blue}{{3}^{1}}\right) \cdot {y}^{1} - z\]

  5. Applied pow10.2

    \[\leadsto \left(\color{blue}{{x}^{1}} \cdot {3}^{1}\right) \cdot {y}^{1} - z\]

  6. Applied pow-prod-down0.2

    \[\leadsto \color{blue}{{\left(x \cdot 3\right)}^{1}} \cdot {y}^{1} - z\]

  7. Applied pow-prod-down0.2

    \[\leadsto \color{blue}{{\left(\left(x \cdot 3\right) \cdot y\right)}^{1}} - z\]

  8. Simplified0.1

    \[\leadsto {\color{blue}{\left(3 \cdot \left(x \cdot y\right)\right)}}^{1} - z\]

  9. Final simplification0.1

    \[\leadsto {\left(3 \cdot \left(x \cdot y\right)\right)}^{1} - z\]

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

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

  (- (* (* x 3) y) z))