Average Error: 0.2 → 0.2
Time: 13.0s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{9 \cdot x}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{9 \cdot x}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r465250 = 1.0;
        double r465251 = x;
        double r465252 = 9.0;
        double r465253 = r465251 * r465252;
        double r465254 = r465250 / r465253;
        double r465255 = r465250 - r465254;
        double r465256 = y;
        double r465257 = 3.0;
        double r465258 = sqrt(r465251);
        double r465259 = r465257 * r465258;
        double r465260 = r465256 / r465259;
        double r465261 = r465255 - r465260;
        return r465261;
}
↓
double f(double x, double y) {
        double r465262 = 1.0;
        double r465263 = 9.0;
        double r465264 = x;
        double r465265 = r465263 * r465264;
        double r465266 = r465262 / r465265;
        double r465267 = r465262 - r465266;
        double r465268 = y;
        double r465269 = 3.0;
        double r465270 = r465268 / r465269;
        double r465271 = sqrt(r465264);
        double r465272 = r465270 / r465271;
        double r465273 = r465267 - r465272;
        return r465273;
}

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 associate-/r*0.2

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

  7. Applied div-inv0.2

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

  8. Applied associate-/l*0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020057 +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)))))