Average Error: 0.2 → 0.2
Time: 24.3s
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 r18627260 = 1.0;
        double r18627261 = x;
        double r18627262 = 9.0;
        double r18627263 = r18627261 * r18627262;
        double r18627264 = r18627260 / r18627263;
        double r18627265 = r18627260 - r18627264;
        double r18627266 = y;
        double r18627267 = 3.0;
        double r18627268 = sqrt(r18627261);
        double r18627269 = r18627267 * r18627268;
        double r18627270 = r18627266 / r18627269;
        double r18627271 = r18627265 - r18627270;
        return r18627271;
}
↓
double f(double x, double y) {
        double r18627272 = 1.0;
        double r18627273 = x;
        double r18627274 = r18627272 / r18627273;
        double r18627275 = 9.0;
        double r18627276 = r18627274 / r18627275;
        double r18627277 = r18627272 - r18627276;
        double r18627278 = y;
        double r18627279 = 3.0;
        double r18627280 = r18627278 / r18627279;
        double r18627281 = sqrt(r18627273);
        double r18627282 = r18627280 / r18627281;
        double r18627283 = r18627277 - r18627282;
        return r18627283;
}

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

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 2019168 
(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)))))