Average Error: 0.2 → 0.2
Time: 3.9s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r404294 = 1.0;
        double r404295 = x;
        double r404296 = 9.0;
        double r404297 = r404295 * r404296;
        double r404298 = r404294 / r404297;
        double r404299 = r404294 - r404298;
        double r404300 = y;
        double r404301 = 3.0;
        double r404302 = sqrt(r404295);
        double r404303 = r404301 * r404302;
        double r404304 = r404300 / r404303;
        double r404305 = r404299 - r404304;
        return r404305;
}
↓
double f(double x, double y) {
        double r404306 = 1.0;
        double r404307 = x;
        double r404308 = r404306 / r404307;
        double r404309 = 9.0;
        double r404310 = r404308 / r404309;
        double r404311 = r404306 - r404310;
        double r404312 = y;
        double r404313 = 3.0;
        double r404314 = r404312 / r404313;
        double r404315 = sqrt(r404307);
        double r404316 = r404314 / r404315;
        double r404317 = r404311 - r404316;
        return r404317;
}

Error

Bits error versus x

Bits error versus y

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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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020049 
(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)))))