Average Error: 0.2 → 0.2
Time: 18.1s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{\frac{\sqrt{x}}{\frac{y}{3}}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{\frac{\sqrt{x}}{\frac{y}{3}}}
double f(double x, double y) {
        double r225986 = 1.0;
        double r225987 = x;
        double r225988 = 9.0;
        double r225989 = r225987 * r225988;
        double r225990 = r225986 / r225989;
        double r225991 = r225986 - r225990;
        double r225992 = y;
        double r225993 = 3.0;
        double r225994 = sqrt(r225987);
        double r225995 = r225993 * r225994;
        double r225996 = r225992 / r225995;
        double r225997 = r225991 - r225996;
        return r225997;
}
↓
double f(double x, double y) {
        double r225998 = 1.0;
        double r225999 = x;
        double r226000 = r225998 / r225999;
        double r226001 = 9.0;
        double r226002 = r226000 / r226001;
        double r226003 = r225998 - r226002;
        double r226004 = 1.0;
        double r226005 = sqrt(r225999);
        double r226006 = y;
        double r226007 = 3.0;
        double r226008 = r226006 / r226007;
        double r226009 = r226005 / r226008;
        double r226010 = r226004 / r226009;
        double r226011 = r226003 - r226010;
        return r226011;
}

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

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

  5. Applied associate-/r*0.2

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

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

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

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

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

  9. Applied times-frac0.2

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

  10. Applied associate-/l*0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(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)))))