Average Error: 0.2 → 0.2
Time: 5.3s
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 r291195 = 1.0;
        double r291196 = x;
        double r291197 = 9.0;
        double r291198 = r291196 * r291197;
        double r291199 = r291195 / r291198;
        double r291200 = r291195 - r291199;
        double r291201 = y;
        double r291202 = 3.0;
        double r291203 = sqrt(r291196);
        double r291204 = r291202 * r291203;
        double r291205 = r291201 / r291204;
        double r291206 = r291200 - r291205;
        return r291206;
}
↓
double f(double x, double y) {
        double r291207 = 1.0;
        double r291208 = x;
        double r291209 = 9.0;
        double r291210 = r291208 * r291209;
        double r291211 = r291207 / r291210;
        double r291212 = r291207 - r291211;
        double r291213 = y;
        double r291214 = 3.0;
        double r291215 = r291213 / r291214;
        double r291216 = sqrt(r291208);
        double r291217 = r291215 / r291216;
        double r291218 = r291212 - r291217;
        return r291218;
}

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 2019354 +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)))))