Average Error: 5.8 → 0.1
Time: 4.4s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{\frac{3 - x}{3}}{\frac{y}{1 - x}}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{\frac{3 - x}{3}}{\frac{y}{1 - x}}
double f(double x, double y) {
        double r726323 = 1.0;
        double r726324 = x;
        double r726325 = r726323 - r726324;
        double r726326 = 3.0;
        double r726327 = r726326 - r726324;
        double r726328 = r726325 * r726327;
        double r726329 = y;
        double r726330 = r726329 * r726326;
        double r726331 = r726328 / r726330;
        return r726331;
}
↓
double f(double x, double y) {
        double r726332 = 3.0;
        double r726333 = x;
        double r726334 = r726332 - r726333;
        double r726335 = r726334 / r726332;
        double r726336 = y;
        double r726337 = 1.0;
        double r726338 = r726337 - r726333;
        double r726339 = r726336 / r726338;
        double r726340 = r726335 / r726339;
        return r726340;
}

Error

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Bits error versus y

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Results

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Target

Original5.8
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.8

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied times-frac0.1

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

  5. Applied clear-num0.2

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

  7. Applied associate-*l/0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

    \[\leadsto \frac{\frac{3 - x}{3}}{\frac{y}{1 - x}}\]

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1 x) y) (/ (- 3 x) 3))

  (/ (* (- 1 x) (- 3 x)) (* y 3)))