Average Error: 0.2 → 0.2
Time: 7.7s
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 r245971 = 1.0;
        double r245972 = x;
        double r245973 = 9.0;
        double r245974 = r245972 * r245973;
        double r245975 = r245971 / r245974;
        double r245976 = r245971 - r245975;
        double r245977 = y;
        double r245978 = 3.0;
        double r245979 = sqrt(r245972);
        double r245980 = r245978 * r245979;
        double r245981 = r245977 / r245980;
        double r245982 = r245976 - r245981;
        return r245982;
}
↓
double f(double x, double y) {
        double r245983 = 1.0;
        double r245984 = x;
        double r245985 = r245983 / r245984;
        double r245986 = 9.0;
        double r245987 = r245985 / r245986;
        double r245988 = r245983 - r245987;
        double r245989 = y;
        double r245990 = 1.0;
        double r245991 = 3.0;
        double r245992 = sqrt(r245984);
        double r245993 = r245991 * r245992;
        double r245994 = r245990 / r245993;
        double r245995 = r245989 * r245994;
        double r245996 = r245988 - r245995;
        return r245996;
}

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)))))