Average Error: 5.2 → 0.1
Time: 10.9s
Precision: 64
\[\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}\]
↓
\[\frac{3.0 - x}{3.0} \cdot \left(\frac{1.0}{y} - \frac{x}{y}\right)\]
\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}
↓
\frac{3.0 - x}{3.0} \cdot \left(\frac{1.0}{y} - \frac{x}{y}\right)
double f(double x, double y) {
        double r32696397 = 1.0;
        double r32696398 = x;
        double r32696399 = r32696397 - r32696398;
        double r32696400 = 3.0;
        double r32696401 = r32696400 - r32696398;
        double r32696402 = r32696399 * r32696401;
        double r32696403 = y;
        double r32696404 = r32696403 * r32696400;
        double r32696405 = r32696402 / r32696404;
        return r32696405;
}
↓
double f(double x, double y) {
        double r32696406 = 3.0;
        double r32696407 = x;
        double r32696408 = r32696406 - r32696407;
        double r32696409 = r32696408 / r32696406;
        double r32696410 = 1.0;
        double r32696411 = y;
        double r32696412 = r32696410 / r32696411;
        double r32696413 = r32696407 / r32696411;
        double r32696414 = r32696412 - r32696413;
        double r32696415 = r32696409 * r32696414;
        return r32696415;
}

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-sub0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 
(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)))