Average Error: 0.4 → 0.6
Time: 16.9s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\left(-\sqrt{x} \cdot 1\right) + \left(\sqrt{\sqrt{x}} \cdot \left(\frac{1}{9 \cdot x} + y\right)\right) \cdot \sqrt{\sqrt{x}}\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
3 \cdot \left(\left(-\sqrt{x} \cdot 1\right) + \left(\sqrt{\sqrt{x}} \cdot \left(\frac{1}{9 \cdot x} + y\right)\right) \cdot \sqrt{\sqrt{x}}\right)
double f(double x, double y) {
        double r20807190 = 3.0;
        double r20807191 = x;
        double r20807192 = sqrt(r20807191);
        double r20807193 = r20807190 * r20807192;
        double r20807194 = y;
        double r20807195 = 1.0;
        double r20807196 = 9.0;
        double r20807197 = r20807191 * r20807196;
        double r20807198 = r20807195 / r20807197;
        double r20807199 = r20807194 + r20807198;
        double r20807200 = r20807199 - r20807195;
        double r20807201 = r20807193 * r20807200;
        return r20807201;
}
↓
double f(double x, double y) {
        double r20807202 = 3.0;
        double r20807203 = x;
        double r20807204 = sqrt(r20807203);
        double r20807205 = 1.0;
        double r20807206 = r20807204 * r20807205;
        double r20807207 = -r20807206;
        double r20807208 = sqrt(r20807204);
        double r20807209 = 9.0;
        double r20807210 = r20807209 * r20807203;
        double r20807211 = r20807205 / r20807210;
        double r20807212 = y;
        double r20807213 = r20807211 + r20807212;
        double r20807214 = r20807208 * r20807213;
        double r20807215 = r20807214 * r20807208;
        double r20807216 = r20807207 + r20807215;
        double r20807217 = r20807202 * r20807216;
        return r20807217;
}

Error

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Results

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Target

Original0.4
Target0.4
Herbie0.6
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

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 sub-neg0.4

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

  6. Applied distribute-lft-in0.4

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

  8. Applied add-sqr-sqrt0.4

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

  9. Applied sqrt-prod0.6

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

  10. Applied associate-*l*0.6

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

  11. Final simplification0.6

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

Reproduce

herbie shell --seed 2019174 
(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)))