Average Error: 0.4 → 0.4
Time: 4.5s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)
double f(double x, double y) {
        double r401236 = 3.0;
        double r401237 = x;
        double r401238 = sqrt(r401237);
        double r401239 = r401236 * r401238;
        double r401240 = y;
        double r401241 = 1.0;
        double r401242 = 9.0;
        double r401243 = r401237 * r401242;
        double r401244 = r401241 / r401243;
        double r401245 = r401240 + r401244;
        double r401246 = r401245 - r401241;
        double r401247 = r401239 * r401246;
        return r401247;
}
↓
double f(double x, double y) {
        double r401248 = 3.0;
        double r401249 = x;
        double r401250 = sqrt(r401249);
        double r401251 = y;
        double r401252 = 1.0;
        double r401253 = 9.0;
        double r401254 = r401249 * r401253;
        double r401255 = r401252 / r401254;
        double r401256 = r401251 + r401255;
        double r401257 = r401256 - r401252;
        double r401258 = r401250 * r401257;
        double r401259 = r401248 * r401258;
        return r401259;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.4
Target0.4
Herbie0.4
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.4

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (* 3 (+ (* y (sqrt x)) (* (- (/ 1 (* x 9)) 1) (sqrt x))))

  (* (* 3 (sqrt x)) (- (+ y (/ 1 (* x 9))) 1)))