Average Error: 5.6 → 0.1
Time: 3.5s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(1 - x\right) \cdot \frac{\frac{3 - x}{3}}{y}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(1 - x\right) \cdot \frac{\frac{3 - x}{3}}{y}
double f(double x, double y) {
        double r780046 = 1.0;
        double r780047 = x;
        double r780048 = r780046 - r780047;
        double r780049 = 3.0;
        double r780050 = r780049 - r780047;
        double r780051 = r780048 * r780050;
        double r780052 = y;
        double r780053 = r780052 * r780049;
        double r780054 = r780051 / r780053;
        return r780054;
}
↓
double f(double x, double y) {
        double r780055 = 1.0;
        double r780056 = x;
        double r780057 = r780055 - r780056;
        double r780058 = 3.0;
        double r780059 = r780058 - r780056;
        double r780060 = r780059 / r780058;
        double r780061 = y;
        double r780062 = r780060 / r780061;
        double r780063 = r780057 * r780062;
        return r780063;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

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. Applied associate-*l*0.2

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020027 
(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)))