Average Error: 5.6 → 0.1
Time: 2.9s
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 r742316 = 1.0;
        double r742317 = x;
        double r742318 = r742316 - r742317;
        double r742319 = 3.0;
        double r742320 = r742319 - r742317;
        double r742321 = r742318 * r742320;
        double r742322 = y;
        double r742323 = r742322 * r742319;
        double r742324 = r742321 / r742323;
        return r742324;
}
↓
double f(double x, double y) {
        double r742325 = 1.0;
        double r742326 = x;
        double r742327 = r742325 - r742326;
        double r742328 = y;
        double r742329 = r742327 / r742328;
        double r742330 = 1.0;
        double r742331 = 3.0;
        double r742332 = r742326 / r742331;
        double r742333 = r742330 - r742332;
        double r742334 = r742329 * r742333;
        return r742334;
}

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)))