Average Error: 5.6 → 0.1
Time: 10.6s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y \cdot \frac{3}{3 - x}}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y \cdot \frac{3}{3 - x}}
double f(double x, double y) {
        double r733536 = 1.0;
        double r733537 = x;
        double r733538 = r733536 - r733537;
        double r733539 = 3.0;
        double r733540 = r733539 - r733537;
        double r733541 = r733538 * r733540;
        double r733542 = y;
        double r733543 = r733542 * r733539;
        double r733544 = r733541 / r733543;
        return r733544;
}
↓
double f(double x, double y) {
        double r733545 = 1.0;
        double r733546 = x;
        double r733547 = r733545 - r733546;
        double r733548 = y;
        double r733549 = 3.0;
        double r733550 = r733549 - r733546;
        double r733551 = r733549 / r733550;
        double r733552 = r733548 * r733551;
        double r733553 = r733547 / r733552;
        return r733553;
}

Error

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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 associate-/l*0.3

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(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)))