Average Error: 5.6 → 0.1
Time: 3.2s
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 r621985 = 1.0;
        double r621986 = x;
        double r621987 = r621985 - r621986;
        double r621988 = 3.0;
        double r621989 = r621988 - r621986;
        double r621990 = r621987 * r621989;
        double r621991 = y;
        double r621992 = r621991 * r621988;
        double r621993 = r621990 / r621992;
        return r621993;
}
↓
double f(double x, double y) {
        double r621994 = 1.0;
        double r621995 = x;
        double r621996 = r621994 - r621995;
        double r621997 = y;
        double r621998 = r621996 / r621997;
        double r621999 = 1.0;
        double r622000 = 3.0;
        double r622001 = r621995 / r622000;
        double r622002 = r621999 - r622001;
        double r622003 = r621998 * r622002;
        return r622003;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

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 +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)))