Average Error: 0.2 → 0.2
Time: 4.0s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r437058 = 1.0;
        double r437059 = x;
        double r437060 = 9.0;
        double r437061 = r437059 * r437060;
        double r437062 = r437058 / r437061;
        double r437063 = r437058 - r437062;
        double r437064 = y;
        double r437065 = 3.0;
        double r437066 = sqrt(r437059);
        double r437067 = r437065 * r437066;
        double r437068 = r437064 / r437067;
        double r437069 = r437063 - r437068;
        return r437069;
}
↓
double f(double x, double y) {
        double r437070 = 1.0;
        double r437071 = x;
        double r437072 = r437070 / r437071;
        double r437073 = 9.0;
        double r437074 = r437072 / r437073;
        double r437075 = r437070 - r437074;
        double r437076 = y;
        double r437077 = 3.0;
        double r437078 = r437076 / r437077;
        double r437079 = sqrt(r437071);
        double r437080 = r437078 / r437079;
        double r437081 = r437075 - r437080;
        return r437081;
}

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. Using strategy rm

  5. Applied associate-/r*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020065 
(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)))))