Average Error: 5.6 → 0.1
Time: 9.5s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(1 - x\right) \cdot \frac{\frac{3 - x}{3}}{y}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(1 - x\right) \cdot \frac{\frac{3 - x}{3}}{y}
double f(double x, double y) {
        double r446278 = 1.0;
        double r446279 = x;
        double r446280 = r446278 - r446279;
        double r446281 = 3.0;
        double r446282 = r446281 - r446279;
        double r446283 = r446280 * r446282;
        double r446284 = y;
        double r446285 = r446284 * r446281;
        double r446286 = r446283 / r446285;
        return r446286;
}
↓
double f(double x, double y) {
        double r446287 = 1.0;
        double r446288 = x;
        double r446289 = r446287 - r446288;
        double r446290 = 3.0;
        double r446291 = r446290 - r446288;
        double r446292 = r446291 / r446290;
        double r446293 = y;
        double r446294 = r446292 / r446293;
        double r446295 = r446289 * r446294;
        return r446295;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.6
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.6

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

  7. Applied div-inv0.2

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

  8. Applied associate-*l*0.2

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019291 
(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)))