Average Error: 0.2 → 0.2
Time: 20.9s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{\frac{\sqrt{x}}{\frac{y}{3}}}\]
\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 r260092 = 1.0;
        double r260093 = x;
        double r260094 = 9.0;
        double r260095 = r260093 * r260094;
        double r260096 = r260092 / r260095;
        double r260097 = r260092 - r260096;
        double r260098 = y;
        double r260099 = 3.0;
        double r260100 = sqrt(r260093);
        double r260101 = r260099 * r260100;
        double r260102 = r260098 / r260101;
        double r260103 = r260097 - r260102;
        return r260103;
}
↓
double f(double x, double y) {
        double r260104 = 1.0;
        double r260105 = x;
        double r260106 = r260104 / r260105;
        double r260107 = 9.0;
        double r260108 = r260106 / r260107;
        double r260109 = r260104 - r260108;
        double r260110 = 1.0;
        double r260111 = sqrt(r260105);
        double r260112 = y;
        double r260113 = 3.0;
        double r260114 = r260112 / r260113;
        double r260115 = r260111 / r260114;
        double r260116 = r260110 / r260115;
        double r260117 = r260109 - r260116;
        return r260117;
}

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)))))