Average Error: 5.2 → 0.1
Time: 13.9s
Precision: 64
\[\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}\]
↓
\[\frac{1.0 - x}{y} \cdot \left(1 - \frac{x}{3.0}\right)\]
\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}
↓
\frac{1.0 - x}{y} \cdot \left(1 - \frac{x}{3.0}\right)
double f(double x, double y) {
        double r30754206 = 1.0;
        double r30754207 = x;
        double r30754208 = r30754206 - r30754207;
        double r30754209 = 3.0;
        double r30754210 = r30754209 - r30754207;
        double r30754211 = r30754208 * r30754210;
        double r30754212 = y;
        double r30754213 = r30754212 * r30754209;
        double r30754214 = r30754211 / r30754213;
        return r30754214;
}
↓
double f(double x, double y) {
        double r30754215 = 1.0;
        double r30754216 = x;
        double r30754217 = r30754215 - r30754216;
        double r30754218 = y;
        double r30754219 = r30754217 / r30754218;
        double r30754220 = 1.0;
        double r30754221 = 3.0;
        double r30754222 = r30754216 / r30754221;
        double r30754223 = r30754220 - r30754222;
        double r30754224 = r30754219 * r30754223;
        return r30754224;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.2
Target0.1
Herbie0.1
\[\frac{1.0 - x}{y} \cdot \frac{3.0 - x}{3.0}\]

Derivation

  1. Initial program 5.2

    \[\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}\]
  2. Using strategy rm

  3. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1.0 - x}{y} \cdot \frac{3.0 - x}{3.0}}\]
  4. Using strategy rm

  5. Applied div-sub0.1

    \[\leadsto \frac{1.0 - x}{y} \cdot \color{blue}{\left(\frac{3.0}{3.0} - \frac{x}{3.0}\right)}\]

  6. Simplified0.1

    \[\leadsto \frac{1.0 - x}{y} \cdot \left(\color{blue}{1} - \frac{x}{3.0}\right)\]

  7. Final simplification0.1

    \[\leadsto \frac{1.0 - x}{y} \cdot \left(1 - \frac{x}{3.0}\right)\]

Reproduce

herbie shell --seed 2019168 
(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)))