Average Error: 0.2 → 0.2
Time: 21.2s
Precision: 64
\[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
↓
\[\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]
\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}
↓
\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}
double f(double x, double y) {
        double r15953283 = 1.0;
        double r15953284 = x;
        double r15953285 = 9.0;
        double r15953286 = r15953284 * r15953285;
        double r15953287 = r15953283 / r15953286;
        double r15953288 = r15953283 - r15953287;
        double r15953289 = y;
        double r15953290 = 3.0;
        double r15953291 = sqrt(r15953284);
        double r15953292 = r15953290 * r15953291;
        double r15953293 = r15953289 / r15953292;
        double r15953294 = r15953288 - r15953293;
        return r15953294;
}
↓
double f(double x, double y) {
        double r15953295 = 1.0;
        double r15953296 = x;
        double r15953297 = r15953295 / r15953296;
        double r15953298 = 9.0;
        double r15953299 = r15953297 / r15953298;
        double r15953300 = r15953295 - r15953299;
        double r15953301 = y;
        double r15953302 = 3.0;
        double r15953303 = r15953301 / r15953302;
        double r15953304 = sqrt(r15953296);
        double r15953305 = r15953303 / r15953304;
        double r15953306 = r15953300 - r15953305;
        return r15953306;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original0.2
Target0.2
Herbie0.2
\[\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]

Derivation

  1. Initial program 0.2

    \[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

    \[\leadsto \left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \color{blue}{\frac{\frac{y}{3.0}}{\sqrt{x}}}\]
  4. Using strategy rm

  5. Applied associate-/r*0.2

    \[\leadsto \left(1.0 - \color{blue}{\frac{\frac{1.0}{x}}{9.0}}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]

  6. Final simplification0.2

    \[\leadsto \left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"

  :herbie-target
  (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))

  (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))