Average Error: 0.4 → 0.4
Time: 21.5s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\right)\]
\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{\frac{1}{x}}{9}\right) - 1\right)\right)
double f(double x, double y) {
        double r26212212 = 3.0;
        double r26212213 = x;
        double r26212214 = sqrt(r26212213);
        double r26212215 = r26212212 * r26212214;
        double r26212216 = y;
        double r26212217 = 1.0;
        double r26212218 = 9.0;
        double r26212219 = r26212213 * r26212218;
        double r26212220 = r26212217 / r26212219;
        double r26212221 = r26212216 + r26212220;
        double r26212222 = r26212221 - r26212217;
        double r26212223 = r26212215 * r26212222;
        return r26212223;
}
↓
double f(double x, double y) {
        double r26212224 = 3.0;
        double r26212225 = x;
        double r26212226 = sqrt(r26212225);
        double r26212227 = y;
        double r26212228 = 1.0;
        double r26212229 = r26212228 / r26212225;
        double r26212230 = 9.0;
        double r26212231 = r26212229 / r26212230;
        double r26212232 = r26212227 + r26212231;
        double r26212233 = r26212232 - r26212228;
        double r26212234 = r26212226 * r26212233;
        double r26212235 = r26212224 * r26212234;
        return r26212235;
}

Error

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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. Using strategy rm

  5. Applied associate-/r*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))