Average Error: 5.7 → 0.2
Time: 3.0s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(1 - x\right) \cdot \left(\frac{3 - x}{3} \cdot \frac{1}{y}\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(1 - x\right) \cdot \left(\frac{3 - x}{3} \cdot \frac{1}{y}\right)
double f(double x, double y) {
        double r221353 = 1.0;
        double r221354 = x;
        double r221355 = r221353 - r221354;
        double r221356 = 3.0;
        double r221357 = r221356 - r221354;
        double r221358 = r221355 * r221357;
        double r221359 = y;
        double r221360 = r221359 * r221356;
        double r221361 = r221358 / r221360;
        return r221361;
}
↓
double f(double x, double y) {
        double r221362 = 1.0;
        double r221363 = x;
        double r221364 = r221362 - r221363;
        double r221365 = 3.0;
        double r221366 = r221365 - r221363;
        double r221367 = r221366 / r221365;
        double r221368 = 1.0;
        double r221369 = y;
        double r221370 = r221368 / r221369;
        double r221371 = r221367 * r221370;
        double r221372 = r221364 * r221371;
        return r221372;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.7
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.7

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

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

  6. Applied associate-*l*0.2

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

  7. Simplified0.1

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

  9. Applied div-inv0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019362 +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)))