Average Error: 5.9 → 0.2
Time: 13.3s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y} \cdot \left(\left(3 - x\right) \cdot \frac{1}{3}\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y} \cdot \left(\left(3 - x\right) \cdot \frac{1}{3}\right)
double f(double x, double y) {
        double r520391 = 1.0;
        double r520392 = x;
        double r520393 = r520391 - r520392;
        double r520394 = 3.0;
        double r520395 = r520394 - r520392;
        double r520396 = r520393 * r520395;
        double r520397 = y;
        double r520398 = r520397 * r520394;
        double r520399 = r520396 / r520398;
        return r520399;
}
↓
double f(double x, double y) {
        double r520400 = 1.0;
        double r520401 = x;
        double r520402 = r520400 - r520401;
        double r520403 = y;
        double r520404 = r520402 / r520403;
        double r520405 = 3.0;
        double r520406 = r520405 - r520401;
        double r520407 = 1.0;
        double r520408 = r520407 / r520405;
        double r520409 = r520406 * r520408;
        double r520410 = r520404 * r520409;
        return r520410;
}

Error

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Bits error versus y

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Results

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Target

Original5.9
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.9

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  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-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019322 
(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)))