Average Error: 5.6 → 0.1
Time: 3.2s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y} \cdot \left(1 - \frac{x}{3}\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y} \cdot \left(1 - \frac{x}{3}\right)
double f(double x, double y) {
        double r751511 = 1.0;
        double r751512 = x;
        double r751513 = r751511 - r751512;
        double r751514 = 3.0;
        double r751515 = r751514 - r751512;
        double r751516 = r751513 * r751515;
        double r751517 = y;
        double r751518 = r751517 * r751514;
        double r751519 = r751516 / r751518;
        return r751519;
}
↓
double f(double x, double y) {
        double r751520 = 1.0;
        double r751521 = x;
        double r751522 = r751520 - r751521;
        double r751523 = y;
        double r751524 = r751522 / r751523;
        double r751525 = 1.0;
        double r751526 = 3.0;
        double r751527 = r751521 / r751526;
        double r751528 = r751525 - r751527;
        double r751529 = r751524 * r751528;
        return r751529;
}

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-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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020001 
(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)))