Average Error: 5.7 → 0.1
Time: 15.1s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{\frac{1 - x}{y}}{\frac{3}{3 - x}}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{\frac{1 - x}{y}}{\frac{3}{3 - x}}
double f(double x, double y) {
        double r544013 = 1.0;
        double r544014 = x;
        double r544015 = r544013 - r544014;
        double r544016 = 3.0;
        double r544017 = r544016 - r544014;
        double r544018 = r544015 * r544017;
        double r544019 = y;
        double r544020 = r544019 * r544016;
        double r544021 = r544018 / r544020;
        return r544021;
}
↓
double f(double x, double y) {
        double r544022 = 1.0;
        double r544023 = x;
        double r544024 = r544022 - r544023;
        double r544025 = y;
        double r544026 = r544024 / r544025;
        double r544027 = 3.0;
        double r544028 = r544027 - r544023;
        double r544029 = r544027 / r544028;
        double r544030 = r544026 / r544029;
        return r544030;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.7
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.7

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

    \[\leadsto \frac{1 - x}{y} \cdot \color{blue}{\frac{1}{\frac{3}{3 - x}}}\]
  6. Using strategy rm

  7. Applied un-div-inv0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(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)))