Average Error: 5.4 → 0.1
Time: 50.5s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(1 - x\right) \cdot \frac{1 - \frac{x}{3}}{y}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(1 - x\right) \cdot \frac{1 - \frac{x}{3}}{y}
double f(double x, double y) {
        double r32318348 = 1.0;
        double r32318349 = x;
        double r32318350 = r32318348 - r32318349;
        double r32318351 = 3.0;
        double r32318352 = r32318351 - r32318349;
        double r32318353 = r32318350 * r32318352;
        double r32318354 = y;
        double r32318355 = r32318354 * r32318351;
        double r32318356 = r32318353 / r32318355;
        return r32318356;
}
↓
double f(double x, double y) {
        double r32318357 = 1.0;
        double r32318358 = x;
        double r32318359 = r32318357 - r32318358;
        double r32318360 = 1.0;
        double r32318361 = 3.0;
        double r32318362 = r32318358 / r32318361;
        double r32318363 = r32318360 - r32318362;
        double r32318364 = y;
        double r32318365 = r32318363 / r32318364;
        double r32318366 = r32318359 * r32318365;
        return r32318366;
}

Error

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Bits error versus y

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Results

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Target

Original5.4
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.4

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  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 div-sub0.1

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

  6. Simplified0.1

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

  8. Applied div-inv0.2

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

  9. Applied associate-*l*0.2

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"

  :herbie-target
  (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))