Average Error: 0.2 → 0.2
Time: 16.1s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{\frac{3 \cdot \sqrt{x}}{y}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{\frac{3 \cdot \sqrt{x}}{y}}
double f(double x, double y) {
        double r249016 = 1.0;
        double r249017 = x;
        double r249018 = 9.0;
        double r249019 = r249017 * r249018;
        double r249020 = r249016 / r249019;
        double r249021 = r249016 - r249020;
        double r249022 = y;
        double r249023 = 3.0;
        double r249024 = sqrt(r249017);
        double r249025 = r249023 * r249024;
        double r249026 = r249022 / r249025;
        double r249027 = r249021 - r249026;
        return r249027;
}
↓
double f(double x, double y) {
        double r249028 = 1.0;
        double r249029 = x;
        double r249030 = r249028 / r249029;
        double r249031 = 9.0;
        double r249032 = r249030 / r249031;
        double r249033 = r249028 - r249032;
        double r249034 = 1.0;
        double r249035 = 3.0;
        double r249036 = sqrt(r249029);
        double r249037 = r249035 * r249036;
        double r249038 = y;
        double r249039 = r249037 / r249038;
        double r249040 = r249034 / r249039;
        double r249041 = r249033 - r249040;
        return r249041;
}

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. Simplified0.2

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

  4. Applied clear-num0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019212 
(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)))))