Average Error: 0.2 → 0.2
Time: 4.2s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r402237 = 1.0;
        double r402238 = x;
        double r402239 = 9.0;
        double r402240 = r402238 * r402239;
        double r402241 = r402237 / r402240;
        double r402242 = r402237 - r402241;
        double r402243 = y;
        double r402244 = 3.0;
        double r402245 = sqrt(r402238);
        double r402246 = r402244 * r402245;
        double r402247 = r402243 / r402246;
        double r402248 = r402242 - r402247;
        return r402248;
}
↓
double f(double x, double y) {
        double r402249 = 1.0;
        double r402250 = x;
        double r402251 = r402249 / r402250;
        double r402252 = 9.0;
        double r402253 = r402251 / r402252;
        double r402254 = r402249 - r402253;
        double r402255 = y;
        double r402256 = 1.0;
        double r402257 = 3.0;
        double r402258 = sqrt(r402250);
        double r402259 = r402257 * r402258;
        double r402260 = r402256 / r402259;
        double r402261 = r402255 * r402260;
        double r402262 = r402254 - r402261;
        return r402262;
}

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

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

  5. Applied div-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(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)))))