Average Error: 5.9 → 0.1
Time: 12.5s
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 r530235 = 1.0;
        double r530236 = x;
        double r530237 = r530235 - r530236;
        double r530238 = 3.0;
        double r530239 = r530238 - r530236;
        double r530240 = r530237 * r530239;
        double r530241 = y;
        double r530242 = r530241 * r530238;
        double r530243 = r530240 / r530242;
        return r530243;
}
↓
double f(double x, double y) {
        double r530244 = 1.0;
        double r530245 = x;
        double r530246 = r530244 - r530245;
        double r530247 = y;
        double r530248 = r530246 / r530247;
        double r530249 = 3.0;
        double r530250 = r530249 - r530245;
        double r530251 = r530249 / r530250;
        double r530252 = r530248 / r530251;
        return r530252;
}

Error

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Bits error versus y

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Results

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Target

Original5.9
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.9

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied associate-/l*0.3

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

  5. Applied *-un-lft-identity0.3

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

  6. Applied times-frac0.1

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

  7. Applied associate-/r*0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019212 +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)))