Average Error: 0.2 → 0.3
Time: 11.5s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}
double f(double x, double y) {
        double r282999 = 1.0;
        double r283000 = x;
        double r283001 = 9.0;
        double r283002 = r283000 * r283001;
        double r283003 = r282999 / r283002;
        double r283004 = r282999 - r283003;
        double r283005 = y;
        double r283006 = 3.0;
        double r283007 = sqrt(r283000);
        double r283008 = r283006 * r283007;
        double r283009 = r283005 / r283008;
        double r283010 = r283004 - r283009;
        return r283010;
}
↓
double f(double x, double y) {
        double r283011 = 1.0;
        double r283012 = x;
        double r283013 = 9.0;
        double r283014 = r283012 * r283013;
        double r283015 = r283011 / r283014;
        double r283016 = r283011 - r283015;
        double r283017 = 1.0;
        double r283018 = 3.0;
        double r283019 = r283017 / r283018;
        double r283020 = y;
        double r283021 = sqrt(r283012);
        double r283022 = r283020 / r283021;
        double r283023 = r283019 * r283022;
        double r283024 = r283016 - r283023;
        return r283024;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original0.2
Target0.2
Herbie0.3
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

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 *-un-lft-identity0.2

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

  4. Applied times-frac0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019325 
(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)))))