Average Error: 5.8 → 0.2
Time: 3.7s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1}{\frac{y}{1 - x}} \cdot \frac{3 - x}{3}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1}{\frac{y}{1 - x}} \cdot \frac{3 - x}{3}
double f(double x, double y) {
        double r677529 = 1.0;
        double r677530 = x;
        double r677531 = r677529 - r677530;
        double r677532 = 3.0;
        double r677533 = r677532 - r677530;
        double r677534 = r677531 * r677533;
        double r677535 = y;
        double r677536 = r677535 * r677532;
        double r677537 = r677534 / r677536;
        return r677537;
}
↓
double f(double x, double y) {
        double r677538 = 1.0;
        double r677539 = y;
        double r677540 = 1.0;
        double r677541 = x;
        double r677542 = r677540 - r677541;
        double r677543 = r677539 / r677542;
        double r677544 = r677538 / r677543;
        double r677545 = 3.0;
        double r677546 = r677545 - r677541;
        double r677547 = r677546 / r677545;
        double r677548 = r677544 * r677547;
        return r677548;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.8
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.8

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  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 clear-num0.2

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{1 - x}}} \cdot \frac{3 - x}{3}\]

  6. Final simplification0.2

    \[\leadsto \frac{1}{\frac{y}{1 - x}} \cdot \frac{3 - x}{3}\]

Reproduce

herbie shell --seed 2020018 
(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)))