Average Error: 1.9 → 1.9
Time: 51.5s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y}} \cdot \sqrt[3]{\frac{\frac{x \cdot e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}}\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y}} \cdot \sqrt[3]{\frac{\frac{x \cdot e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r3651557 = x;
        double r3651558 = y;
        double r3651559 = z;
        double r3651560 = log(r3651559);
        double r3651561 = r3651558 * r3651560;
        double r3651562 = t;
        double r3651563 = 1.0;
        double r3651564 = r3651562 - r3651563;
        double r3651565 = a;
        double r3651566 = log(r3651565);
        double r3651567 = r3651564 * r3651566;
        double r3651568 = r3651561 + r3651567;
        double r3651569 = b;
        double r3651570 = r3651568 - r3651569;
        double r3651571 = exp(r3651570);
        double r3651572 = r3651557 * r3651571;
        double r3651573 = r3651572 / r3651558;
        return r3651573;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3651574 = x;
        double r3651575 = exp(1.0);
        double r3651576 = z;
        double r3651577 = log(r3651576);
        double r3651578 = y;
        double r3651579 = r3651577 * r3651578;
        double r3651580 = t;
        double r3651581 = 1.0;
        double r3651582 = r3651580 - r3651581;
        double r3651583 = a;
        double r3651584 = log(r3651583);
        double r3651585 = r3651582 * r3651584;
        double r3651586 = r3651579 + r3651585;
        double r3651587 = b;
        double r3651588 = r3651586 - r3651587;
        double r3651589 = pow(r3651575, r3651588);
        double r3651590 = r3651574 * r3651589;
        double r3651591 = r3651590 / r3651578;
        double r3651592 = cbrt(r3651591);
        double r3651593 = exp(r3651588);
        double r3651594 = r3651574 * r3651593;
        double r3651595 = cbrt(r3651578);
        double r3651596 = r3651595 * r3651595;
        double r3651597 = r3651594 / r3651596;
        double r3651598 = r3651597 / r3651595;
        double r3651599 = cbrt(r3651598);
        double r3651600 = r3651592 * r3651599;
        double r3651601 = r3651592 * r3651600;
        return r3651601;
}

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 1.9

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

  3. Applied *-un-lft-identity1.9

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

  4. Applied *-un-lft-identity1.9

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

  5. Applied distribute-lft-out--1.9

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

  6. Applied exp-prod1.9

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

  7. Simplified1.9

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

  9. Applied add-cube-cbrt1.9

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

  11. Applied e-exp-11.9

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

  12. Applied pow-exp1.9

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

  14. Applied add-cube-cbrt1.9

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

  15. Applied associate-/r*1.9

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

  16. Final simplification1.9

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

Reproduce

herbie shell --seed 2019135 +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))