Average Error: 5.2 → 0.1
Time: 17.5s
Precision: 64
\[\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}\]
↓
\[\frac{\frac{3.0 - x}{3.0}}{y} \cdot \left(1.0 - x\right)\]
\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}
↓
\frac{\frac{3.0 - x}{3.0}}{y} \cdot \left(1.0 - x\right)
double f(double x, double y) {
        double r28081464 = 1.0;
        double r28081465 = x;
        double r28081466 = r28081464 - r28081465;
        double r28081467 = 3.0;
        double r28081468 = r28081467 - r28081465;
        double r28081469 = r28081466 * r28081468;
        double r28081470 = y;
        double r28081471 = r28081470 * r28081467;
        double r28081472 = r28081469 / r28081471;
        return r28081472;
}
↓
double f(double x, double y) {
        double r28081473 = 3.0;
        double r28081474 = x;
        double r28081475 = r28081473 - r28081474;
        double r28081476 = r28081475 / r28081473;
        double r28081477 = y;
        double r28081478 = r28081476 / r28081477;
        double r28081479 = 1.0;
        double r28081480 = r28081479 - r28081474;
        double r28081481 = r28081478 * r28081480;
        return r28081481;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.2
Target0.1
Herbie0.1
\[\frac{1.0 - x}{y} \cdot \frac{3.0 - x}{3.0}\]

Derivation

  1. Initial program 5.2

    \[\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}\]
  2. Using strategy rm

  3. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1.0 - x}{y} \cdot \frac{3.0 - x}{3.0}}\]
  4. Using strategy rm

  5. Applied div-inv0.2

    \[\leadsto \color{blue}{\left(\left(1.0 - x\right) \cdot \frac{1}{y}\right)} \cdot \frac{3.0 - x}{3.0}\]

  6. Applied associate-*l*0.2

    \[\leadsto \color{blue}{\left(1.0 - x\right) \cdot \left(\frac{1}{y} \cdot \frac{3.0 - x}{3.0}\right)}\]

  7. Simplified0.1

    \[\leadsto \left(1.0 - x\right) \cdot \color{blue}{\frac{\frac{3.0 - x}{3.0}}{y}}\]

  8. Final simplification0.1

    \[\leadsto \frac{\frac{3.0 - x}{3.0}}{y} \cdot \left(1.0 - x\right)\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(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)))