Average Error: 5.9 → 0.1
Time: 2.7s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y} \cdot \frac{3 - x}{3}
double f(double x, double y) {
        double r637186 = 1.0;
        double r637187 = x;
        double r637188 = r637186 - r637187;
        double r637189 = 3.0;
        double r637190 = r637189 - r637187;
        double r637191 = r637188 * r637190;
        double r637192 = y;
        double r637193 = r637192 * r637189;
        double r637194 = r637191 / r637193;
        return r637194;
}
↓
double f(double x, double y) {
        double r637195 = 1.0;
        double r637196 = x;
        double r637197 = r637195 - r637196;
        double r637198 = y;
        double r637199 = r637197 / r637198;
        double r637200 = 3.0;
        double r637201 = r637200 - r637196;
        double r637202 = r637201 / r637200;
        double r637203 = r637199 * r637202;
        return r637203;
}

Error

Bits error versus x

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 times-frac0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019354 
(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)))