Average Error: 5.8 → 0.1
Time: 3.6s
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 r598147 = 1.0;
        double r598148 = x;
        double r598149 = r598147 - r598148;
        double r598150 = 3.0;
        double r598151 = r598150 - r598148;
        double r598152 = r598149 * r598151;
        double r598153 = y;
        double r598154 = r598153 * r598150;
        double r598155 = r598152 / r598154;
        return r598155;
}
↓
double f(double x, double y) {
        double r598156 = 1.0;
        double r598157 = x;
        double r598158 = r598156 - r598157;
        double r598159 = y;
        double r598160 = r598158 / r598159;
        double r598161 = 3.0;
        double r598162 = r598161 - r598157;
        double r598163 = r598162 / r598161;
        double r598164 = r598160 * r598163;
        return r598164;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.8
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.8

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  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 2020021 +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)))