Average Error: 0.1 → 0.1
Time: 7.5s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left({\left({y}^{\frac{1}{3}}\right)}^{\frac{2}{3}} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right)\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left({\left({y}^{\frac{1}{3}}\right)}^{\frac{2}{3}} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right)\right) - y\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r127556 = x;
        double r127557 = y;
        double r127558 = log(r127557);
        double r127559 = r127556 * r127558;
        double r127560 = r127559 - r127557;
        double r127561 = z;
        double r127562 = r127560 - r127561;
        double r127563 = t;
        double r127564 = log(r127563);
        double r127565 = r127562 + r127564;
        return r127565;
}
↓
double f(double x, double y, double z, double t) {
        double r127566 = x;
        double r127567 = 2.0;
        double r127568 = y;
        double r127569 = cbrt(r127568);
        double r127570 = log(r127569);
        double r127571 = r127567 * r127570;
        double r127572 = r127566 * r127571;
        double r127573 = 0.3333333333333333;
        double r127574 = pow(r127568, r127573);
        double r127575 = 0.6666666666666666;
        double r127576 = pow(r127574, r127575);
        double r127577 = pow(r127569, r127573);
        double r127578 = r127576 * r127577;
        double r127579 = log(r127578);
        double r127580 = r127566 * r127579;
        double r127581 = r127572 + r127580;
        double r127582 = r127581 - r127568;
        double r127583 = z;
        double r127584 = r127582 - r127583;
        double r127585 = t;
        double r127586 = log(r127585);
        double r127587 = r127584 + r127586;
        return r127587;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(x \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} - y\right) - z\right) + \log t\]

  4. Applied log-prod0.1

    \[\leadsto \left(\left(x \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} - y\right) - z\right) + \log t\]

  5. Applied distribute-lft-in0.1

    \[\leadsto \left(\left(\color{blue}{\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right)} - y\right) - z\right) + \log t\]

  6. Simplified0.1

    \[\leadsto \left(\left(\left(\color{blue}{x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)} + x \cdot \log \left(\sqrt[3]{y}\right)\right) - y\right) - z\right) + \log t\]
  7. Using strategy rm

  8. Applied pow1/30.1

    \[\leadsto \left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \color{blue}{\left({y}^{\frac{1}{3}}\right)}\right) - y\right) - z\right) + \log t\]
  9. Using strategy rm

  10. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \color{blue}{\left(\left(\sqrt[3]{{y}^{\frac{1}{3}}} \cdot \sqrt[3]{{y}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{{y}^{\frac{1}{3}}}\right)}\right) - y\right) - z\right) + \log t\]

  11. Simplified0.1

    \[\leadsto \left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\color{blue}{{\left({y}^{\frac{1}{3}}\right)}^{\frac{2}{3}}} \cdot \sqrt[3]{{y}^{\frac{1}{3}}}\right)\right) - y\right) - z\right) + \log t\]

  12. Simplified0.1

    \[\leadsto \left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left({\left({y}^{\frac{1}{3}}\right)}^{\frac{2}{3}} \cdot \color{blue}{{\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}}\right)\right) - y\right) - z\right) + \log t\]

  13. Final simplification0.1

    \[\leadsto \left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left({\left({y}^{\frac{1}{3}}\right)}^{\frac{2}{3}} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right)\right) - y\right) - z\right) + \log t\]

Reproduce

herbie shell --seed 2019347 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))