Average Error: 0.3 → 0.2
Time: 1.6s
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 r730510 = x;
        double r730511 = y;
        double r730512 = 3.0;
        double r730513 = r730511 * r730512;
        double r730514 = r730510 / r730513;
        return r730514;
}
↓
double f(double x, double y) {
        double r730515 = x;
        double r730516 = 3.0;
        double r730517 = r730515 / r730516;
        double r730518 = y;
        double r730519 = r730517 / r730518;
        return r730519;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 0.3

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

  3. Applied *-un-lft-identity0.3

    \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot 3}\]

  4. Applied times-frac0.3

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

  6. Applied pow10.3

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

  7. Applied pow10.3

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

  8. Applied pow-prod-down0.3

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 +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)))