Average Error: 5.6 → 0.2
Time: 2.4s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(\left(1 - x\right) \cdot \frac{1}{y}\right) \cdot \frac{3 - x}{3}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(\left(1 - x\right) \cdot \frac{1}{y}\right) \cdot \frac{3 - x}{3}
double f(double x, double y) {
        double r711285 = 1.0;
        double r711286 = x;
        double r711287 = r711285 - r711286;
        double r711288 = 3.0;
        double r711289 = r711288 - r711286;
        double r711290 = r711287 * r711289;
        double r711291 = y;
        double r711292 = r711291 * r711288;
        double r711293 = r711290 / r711292;
        return r711293;
}
↓
double f(double x, double y) {
        double r711294 = 1.0;
        double r711295 = x;
        double r711296 = r711294 - r711295;
        double r711297 = 1.0;
        double r711298 = y;
        double r711299 = r711297 / r711298;
        double r711300 = r711296 * r711299;
        double r711301 = 3.0;
        double r711302 = r711301 - r711295;
        double r711303 = r711302 / r711301;
        double r711304 = r711300 * r711303;
        return r711304;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.6
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.6

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  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-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020062 
(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)))