Average Error: 5.9 → 0.1
Time: 13.2s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{3 - x}{3} \cdot \frac{1 - x}{y}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{3 - x}{3} \cdot \frac{1 - x}{y}
double f(double x, double y) {
        double r490196 = 1.0;
        double r490197 = x;
        double r490198 = r490196 - r490197;
        double r490199 = 3.0;
        double r490200 = r490199 - r490197;
        double r490201 = r490198 * r490200;
        double r490202 = y;
        double r490203 = r490202 * r490199;
        double r490204 = r490201 / r490203;
        return r490204;
}
↓
double f(double x, double y) {
        double r490205 = 3.0;
        double r490206 = x;
        double r490207 = r490205 - r490206;
        double r490208 = r490207 / r490205;
        double r490209 = 1.0;
        double r490210 = r490209 - r490206;
        double r490211 = y;
        double r490212 = r490210 / r490211;
        double r490213 = r490208 * r490212;
        return r490213;
}

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. Using strategy rm

  5. Applied pow10.1

    \[\leadsto \color{blue}{{\left(\frac{1 - x}{y}\right)}^{1}} \cdot \frac{3 - x}{3}\]

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(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)))