Average Error: 0.3 → 0.2
Time: 23.3s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{\frac{x}{3}}{y}\]
\frac{x}{y \cdot 3}
↓
\frac{\frac{x}{3}}{y}
double f(double x, double y) {
        double r395667 = x;
        double r395668 = y;
        double r395669 = 3.0;
        double r395670 = r395668 * r395669;
        double r395671 = r395667 / r395670;
        return r395671;
}
↓
double f(double x, double y) {
        double r395672 = x;
        double r395673 = 3.0;
        double r395674 = r395672 / r395673;
        double r395675 = y;
        double r395676 = r395674 / r395675;
        return r395676;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.3
Target0.3
Herbie0.2
\[\frac{\frac{x}{y}}{3}\]

Derivation

  1. Initial program 0.3

    \[\frac{x}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied div-inv0.4

    \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot 3}}\]
  4. Using strategy rm

  5. Applied pow10.4

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

  6. Applied pow10.4

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

  7. Applied pow-prod-down0.4

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

  8. Simplified0.2

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

  9. Final simplification0.2

    \[\leadsto \frac{\frac{x}{3}}{y}\]

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

  :herbie-target
  (/ (/ x y) 3)

  (/ x (* y 3)))