Average Error: 0.2 → 0.2
Time: 11.6s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r406280 = 1.0;
        double r406281 = x;
        double r406282 = 9.0;
        double r406283 = r406281 * r406282;
        double r406284 = r406280 / r406283;
        double r406285 = r406280 - r406284;
        double r406286 = y;
        double r406287 = 3.0;
        double r406288 = sqrt(r406281);
        double r406289 = r406287 * r406288;
        double r406290 = r406286 / r406289;
        double r406291 = r406285 - r406290;
        return r406291;
}
↓
double f(double x, double y) {
        double r406292 = 1.0;
        double r406293 = x;
        double r406294 = 9.0;
        double r406295 = r406293 * r406294;
        double r406296 = r406292 / r406295;
        double r406297 = r406292 - r406296;
        double r406298 = y;
        double r406299 = 3.0;
        double r406300 = r406298 / r406299;
        double r406301 = sqrt(r406293);
        double r406302 = r406300 / r406301;
        double r406303 = r406297 - r406302;
        return r406303;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020100 
(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)))))