Average Error: 5.7 → 0.1
Time: 14.5s
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 r34415245 = 1.0;
        double r34415246 = x;
        double r34415247 = r34415245 - r34415246;
        double r34415248 = 3.0;
        double r34415249 = r34415248 - r34415246;
        double r34415250 = r34415247 * r34415249;
        double r34415251 = y;
        double r34415252 = r34415251 * r34415248;
        double r34415253 = r34415250 / r34415252;
        return r34415253;
}
↓
double f(double x, double y) {
        double r34415254 = 1.0;
        double r34415255 = x;
        double r34415256 = r34415254 - r34415255;
        double r34415257 = y;
        double r34415258 = r34415256 / r34415257;
        double r34415259 = 1.0;
        double r34415260 = 3.0;
        double r34415261 = r34415255 / r34415260;
        double r34415262 = r34415259 - r34415261;
        double r34415263 = r34415258 * r34415262;
        return r34415263;
}

Error

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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 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 2019179 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"

  :herbie-target
  (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))