Average Error: 0.2 → 0.2
Time: 4.9s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3} \cdot \frac{1}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3} \cdot \frac{1}{\sqrt{x}}
double f(double x, double y) {
        double r375318 = 1.0;
        double r375319 = x;
        double r375320 = 9.0;
        double r375321 = r375319 * r375320;
        double r375322 = r375318 / r375321;
        double r375323 = r375318 - r375322;
        double r375324 = y;
        double r375325 = 3.0;
        double r375326 = sqrt(r375319);
        double r375327 = r375325 * r375326;
        double r375328 = r375324 / r375327;
        double r375329 = r375323 - r375328;
        return r375329;
}
↓
double f(double x, double y) {
        double r375330 = 1.0;
        double r375331 = x;
        double r375332 = r375330 / r375331;
        double r375333 = 9.0;
        double r375334 = r375332 / r375333;
        double r375335 = r375330 - r375334;
        double r375336 = y;
        double r375337 = 3.0;
        double r375338 = r375336 / r375337;
        double r375339 = 1.0;
        double r375340 = sqrt(r375331);
        double r375341 = r375339 / r375340;
        double r375342 = r375338 * r375341;
        double r375343 = r375335 - r375342;
        return r375343;
}

Error

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Results

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Target

Original0.2
Target0.2
Herbie0.2
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

Derivation

  1. Initial program 0.2

    \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

    \[\leadsto \left(1 - \color{blue}{\frac{\frac{1}{x}}{9}}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.2

    \[\leadsto \left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{\color{blue}{1 \cdot y}}{3 \cdot \sqrt{x}}\]

  6. Applied times-frac0.3

    \[\leadsto \left(1 - \frac{\frac{1}{x}}{9}\right) - \color{blue}{\frac{1}{3} \cdot \frac{y}{\sqrt{x}}}\]
  7. Using strategy rm

  8. Applied div-inv0.3

    \[\leadsto \left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{3} \cdot \color{blue}{\left(y \cdot \frac{1}{\sqrt{x}}\right)}\]

  9. Applied associate-*r*0.3

    \[\leadsto \left(1 - \frac{\frac{1}{x}}{9}\right) - \color{blue}{\left(\frac{1}{3} \cdot y\right) \cdot \frac{1}{\sqrt{x}}}\]

  10. Simplified0.2

    \[\leadsto \left(1 - \frac{\frac{1}{x}}{9}\right) - \color{blue}{\frac{y}{3}} \cdot \frac{1}{\sqrt{x}}\]

  11. Final simplification0.2

    \[\leadsto \left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3} \cdot \frac{1}{\sqrt{x}}\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (- (- 1 (/ (/ 1 x) 9)) (/ y (* 3 (sqrt x))))

  (- (- 1 (/ 1 (* x 9))) (/ y (* 3 (sqrt x)))))