Average Error: 0.2 → 0.3
Time: 10.3s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}
double f(double x, double y) {
        double r481273 = 1.0;
        double r481274 = x;
        double r481275 = 9.0;
        double r481276 = r481274 * r481275;
        double r481277 = r481273 / r481276;
        double r481278 = r481273 - r481277;
        double r481279 = y;
        double r481280 = 3.0;
        double r481281 = sqrt(r481274);
        double r481282 = r481280 * r481281;
        double r481283 = r481279 / r481282;
        double r481284 = r481278 - r481283;
        return r481284;
}
↓
double f(double x, double y) {
        double r481285 = 1.0;
        double r481286 = x;
        double r481287 = r481285 / r481286;
        double r481288 = 9.0;
        double r481289 = r481287 / r481288;
        double r481290 = r481285 - r481289;
        double r481291 = 1.0;
        double r481292 = 3.0;
        double r481293 = r481291 / r481292;
        double r481294 = y;
        double r481295 = sqrt(r481286);
        double r481296 = r481294 / r481295;
        double r481297 = r481293 * r481296;
        double r481298 = r481290 - r481297;
        return r481298;
}

Error

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Bits error versus y

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Results

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Target

Original0.2
Target0.2
Herbie0.3
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

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 *-un-lft-identity0.2

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

  6. Applied times-frac0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020045 
(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)))))