Average Error: 0.4 → 0.4
Time: 5.2s
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 r511212 = 3.0;
        double r511213 = x;
        double r511214 = sqrt(r511213);
        double r511215 = r511212 * r511214;
        double r511216 = y;
        double r511217 = 1.0;
        double r511218 = 9.0;
        double r511219 = r511213 * r511218;
        double r511220 = r511217 / r511219;
        double r511221 = r511216 + r511220;
        double r511222 = r511221 - r511217;
        double r511223 = r511215 * r511222;
        return r511223;
}
↓
double f(double x, double y) {
        double r511224 = 3.0;
        double r511225 = x;
        double r511226 = sqrt(r511225);
        double r511227 = y;
        double r511228 = 1.0;
        double r511229 = 9.0;
        double r511230 = r511225 * r511229;
        double r511231 = r511228 / r511230;
        double r511232 = r511227 + r511231;
        double r511233 = r511232 - r511228;
        double r511234 = r511226 * r511233;
        double r511235 = r511224 * r511234;
        return r511235;
}

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 2020100 +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)))