Average Error: 0.2 → 0.2
Time: 4.1s
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 r354976 = 1.0;
        double r354977 = x;
        double r354978 = 9.0;
        double r354979 = r354977 * r354978;
        double r354980 = r354976 / r354979;
        double r354981 = r354976 - r354980;
        double r354982 = y;
        double r354983 = 3.0;
        double r354984 = sqrt(r354977);
        double r354985 = r354983 * r354984;
        double r354986 = r354982 / r354985;
        double r354987 = r354981 - r354986;
        return r354987;
}
↓
double f(double x, double y) {
        double r354988 = 1.0;
        double r354989 = x;
        double r354990 = 9.0;
        double r354991 = r354989 * r354990;
        double r354992 = r354988 / r354991;
        double r354993 = r354988 - r354992;
        double r354994 = y;
        double r354995 = 3.0;
        double r354996 = r354994 / r354995;
        double r354997 = sqrt(r354989);
        double r354998 = r354996 / r354997;
        double r354999 = r354993 - r354998;
        return r354999;
}

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 2020002 
(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)))))