Average Error: 2.0 → 2.0
Time: 49.7s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(\sqrt[3]{\frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right)}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)}}{y}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\left(\sqrt[3]{\frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right)}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)}}{y}}
double f(double x, double y, double z, double t, double a, double b) {
        double r3043561 = x;
        double r3043562 = y;
        double r3043563 = z;
        double r3043564 = log(r3043563);
        double r3043565 = r3043562 * r3043564;
        double r3043566 = t;
        double r3043567 = 1.0;
        double r3043568 = r3043566 - r3043567;
        double r3043569 = a;
        double r3043570 = log(r3043569);
        double r3043571 = r3043568 * r3043570;
        double r3043572 = r3043565 + r3043571;
        double r3043573 = b;
        double r3043574 = r3043572 - r3043573;
        double r3043575 = exp(r3043574);
        double r3043576 = r3043561 * r3043575;
        double r3043577 = r3043576 / r3043562;
        return r3043577;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3043578 = x;
        double r3043579 = a;
        double r3043580 = log(r3043579);
        double r3043581 = t;
        double r3043582 = 1.0;
        double r3043583 = r3043581 - r3043582;
        double r3043584 = r3043580 * r3043583;
        double r3043585 = z;
        double r3043586 = log(r3043585);
        double r3043587 = y;
        double r3043588 = r3043586 * r3043587;
        double r3043589 = r3043584 + r3043588;
        double r3043590 = b;
        double r3043591 = r3043589 - r3043590;
        double r3043592 = exp(r3043591);
        double r3043593 = sqrt(r3043592);
        double r3043594 = r3043593 * r3043593;
        double r3043595 = r3043578 * r3043594;
        double r3043596 = r3043595 / r3043587;
        double r3043597 = cbrt(r3043596);
        double r3043598 = r3043578 * r3043592;
        double r3043599 = r3043598 / r3043587;
        double r3043600 = cbrt(r3043599);
        double r3043601 = r3043597 * r3043600;
        double r3043602 = exp(1.0);
        double r3043603 = pow(r3043602, r3043591);
        double r3043604 = r3043578 * r3043603;
        double r3043605 = r3043604 / r3043587;
        double r3043606 = cbrt(r3043605);
        double r3043607 = r3043601 * r3043606;
        return r3043607;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.0

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt2.0

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity2.0

    \[\leadsto \left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot e^{\color{blue}{1 \cdot \left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}{y}}\]

  6. Applied exp-prod2.0

    \[\leadsto \left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot \color{blue}{{\left(e^{1}\right)}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}{y}}\]

  7. Simplified2.0

    \[\leadsto \left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot {\color{blue}{e}}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y}}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt2.0

    \[\leadsto \left(\sqrt[3]{\frac{x \cdot \color{blue}{\left(\sqrt{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot {e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y}}\]

  10. Final simplification2.0

    \[\leadsto \left(\sqrt[3]{\frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right)}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)}}{y}}\]

Reproduce

herbie shell --seed 2019133 +o rules:numerics
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))