Average Error: 0.2 → 0.2
Time: 12.8s
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 r2088 = 1.0;
        double r2089 = x;
        double r2090 = 9.0;
        double r2091 = r2089 * r2090;
        double r2092 = r2088 / r2091;
        double r2093 = r2088 - r2092;
        double r2094 = y;
        double r2095 = 3.0;
        double r2096 = sqrt(r2089);
        double r2097 = r2095 * r2096;
        double r2098 = r2094 / r2097;
        double r2099 = r2093 - r2098;
        return r2099;
}
↓
double f(double x, double y) {
        double r2100 = 1.0;
        double r2101 = x;
        double r2102 = 9.0;
        double r2103 = r2101 * r2102;
        double r2104 = r2100 / r2103;
        double r2105 = r2100 - r2104;
        double r2106 = y;
        double r2107 = 3.0;
        double r2108 = r2106 / r2107;
        double r2109 = sqrt(r2101);
        double r2110 = r2108 / r2109;
        double r2111 = r2105 - r2110;
        return r2111;
}

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 2020025 +o rules:numerics
(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)))))