Average Error: 0.2 → 0.2
Time: 4.9s
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 r570205 = 1.0;
        double r570206 = x;
        double r570207 = 9.0;
        double r570208 = r570206 * r570207;
        double r570209 = r570205 / r570208;
        double r570210 = r570205 - r570209;
        double r570211 = y;
        double r570212 = 3.0;
        double r570213 = sqrt(r570206);
        double r570214 = r570212 * r570213;
        double r570215 = r570211 / r570214;
        double r570216 = r570210 - r570215;
        return r570216;
}
↓
double f(double x, double y) {
        double r570217 = 1.0;
        double r570218 = x;
        double r570219 = r570217 / r570218;
        double r570220 = 9.0;
        double r570221 = r570219 / r570220;
        double r570222 = r570217 - r570221;
        double r570223 = y;
        double r570224 = 3.0;
        double r570225 = r570223 / r570224;
        double r570226 = sqrt(r570218);
        double r570227 = r570225 / r570226;
        double r570228 = r570222 - r570227;
        return r570228;
}

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

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

  5. Applied associate-/r*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020034 +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)))))