Average Error: 0.4 → 0.4
Time: 17.0s
Precision: 64
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[\left(1.0 \cdot \sqrt{x}\right) \cdot \left(-3.0\right) + \sqrt{x} \cdot \left(\left(\frac{1.0}{9.0 \cdot x} + y\right) \cdot 3.0\right)\]
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)
↓
\left(1.0 \cdot \sqrt{x}\right) \cdot \left(-3.0\right) + \sqrt{x} \cdot \left(\left(\frac{1.0}{9.0 \cdot x} + y\right) \cdot 3.0\right)
double f(double x, double y) {
        double r18644094 = 3.0;
        double r18644095 = x;
        double r18644096 = sqrt(r18644095);
        double r18644097 = r18644094 * r18644096;
        double r18644098 = y;
        double r18644099 = 1.0;
        double r18644100 = 9.0;
        double r18644101 = r18644095 * r18644100;
        double r18644102 = r18644099 / r18644101;
        double r18644103 = r18644098 + r18644102;
        double r18644104 = r18644103 - r18644099;
        double r18644105 = r18644097 * r18644104;
        return r18644105;
}
↓
double f(double x, double y) {
        double r18644106 = 1.0;
        double r18644107 = x;
        double r18644108 = sqrt(r18644107);
        double r18644109 = r18644106 * r18644108;
        double r18644110 = 3.0;
        double r18644111 = -r18644110;
        double r18644112 = r18644109 * r18644111;
        double r18644113 = 9.0;
        double r18644114 = r18644113 * r18644107;
        double r18644115 = r18644106 / r18644114;
        double r18644116 = y;
        double r18644117 = r18644115 + r18644116;
        double r18644118 = r18644117 * r18644110;
        double r18644119 = r18644108 * r18644118;
        double r18644120 = r18644112 + r18644119;
        return r18644120;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original0.4
Target0.4
Herbie0.4
\[3.0 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1.0}{x \cdot 9.0} - 1.0\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.4

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \sqrt[3]{3.0}\right)} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)\]

  6. Applied associate-*l*0.6

    \[\leadsto \color{blue}{\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \left(\sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)\right)}\]
  7. Using strategy rm

  8. Applied sub-neg0.6

    \[\leadsto \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \left(\sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \color{blue}{\left(\left(y + \frac{1.0}{x \cdot 9.0}\right) + \left(-1.0\right)\right)}\right)\right)\]

  9. Applied distribute-lft-in0.6

    \[\leadsto \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \left(\sqrt[3]{3.0} \cdot \color{blue}{\left(\sqrt{x} \cdot \left(y + \frac{1.0}{x \cdot 9.0}\right) + \sqrt{x} \cdot \left(-1.0\right)\right)}\right)\]

  10. Applied distribute-lft-in0.6

    \[\leadsto \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \color{blue}{\left(\sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \left(y + \frac{1.0}{x \cdot 9.0}\right)\right) + \sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \left(-1.0\right)\right)\right)}\]

  11. Applied distribute-lft-in0.6

    \[\leadsto \color{blue}{\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \left(\sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \left(y + \frac{1.0}{x \cdot 9.0}\right)\right)\right) + \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \left(\sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \left(-1.0\right)\right)\right)}\]

  12. Simplified0.5

    \[\leadsto \color{blue}{\left(3.0 \cdot \left(\frac{1.0}{9.0 \cdot x} + y\right)\right) \cdot \sqrt{x}} + \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \left(\sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \left(-1.0\right)\right)\right)\]

  13. Simplified0.4

    \[\leadsto \left(3.0 \cdot \left(\frac{1.0}{9.0 \cdot x} + y\right)\right) \cdot \sqrt{x} + \color{blue}{\left(\sqrt{x} \cdot 1.0\right) \cdot \left(-3.0\right)}\]

  14. Final simplification0.4

    \[\leadsto \left(1.0 \cdot \sqrt{x}\right) \cdot \left(-3.0\right) + \sqrt{x} \cdot \left(\left(\frac{1.0}{9.0 \cdot x} + y\right) \cdot 3.0\right)\]

Reproduce

herbie shell --seed 2019163 
(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)))