Average Error: 1.8 → 1.8
Time: 49.3s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\sqrt[3]{\frac{\left(e^{1.0 \cdot \log \left(\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\frac{1}{a}}\right)} \cdot e^{1.0 \cdot \log \left({a}^{\frac{-1}{3}}\right) - \left(\left(t \cdot \log \left(\frac{1}{a}\right) + b\right) + \log \left(\frac{1}{z}\right) \cdot y\right)}\right) \cdot x}{y}} \cdot \left(\sqrt[3]{\frac{\left(e^{1.0 \cdot \log \left(\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\frac{1}{a}}\right)} \cdot e^{1.0 \cdot \log \left({a}^{\frac{-1}{3}}\right) - \left(\left(t \cdot \log \left(\frac{1}{a}\right) + b\right) + \log \left(\frac{1}{z}\right) \cdot y\right)}\right) \cdot x}{y}} \cdot \sqrt[3]{\frac{\left(e^{1.0 \cdot \log \left(\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\frac{1}{a}}\right)} \cdot e^{1.0 \cdot \log \left({a}^{\frac{-1}{3}}\right) - \left(\left(t \cdot \log \left(\frac{1}{a}\right) + b\right) + \log \left(\frac{1}{z}\right) \cdot y\right)}\right) \cdot x}{y}}\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\sqrt[3]{\frac{\left(e^{1.0 \cdot \log \left(\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\frac{1}{a}}\right)} \cdot e^{1.0 \cdot \log \left({a}^{\frac{-1}{3}}\right) - \left(\left(t \cdot \log \left(\frac{1}{a}\right) + b\right) + \log \left(\frac{1}{z}\right) \cdot y\right)}\right) \cdot x}{y}} \cdot \left(\sqrt[3]{\frac{\left(e^{1.0 \cdot \log \left(\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\frac{1}{a}}\right)} \cdot e^{1.0 \cdot \log \left({a}^{\frac{-1}{3}}\right) - \left(\left(t \cdot \log \left(\frac{1}{a}\right) + b\right) + \log \left(\frac{1}{z}\right) \cdot y\right)}\right) \cdot x}{y}} \cdot \sqrt[3]{\frac{\left(e^{1.0 \cdot \log \left(\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\frac{1}{a}}\right)} \cdot e^{1.0 \cdot \log \left({a}^{\frac{-1}{3}}\right) - \left(\left(t \cdot \log \left(\frac{1}{a}\right) + b\right) + \log \left(\frac{1}{z}\right) \cdot y\right)}\right) \cdot x}{y}}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r2462539 = x;
        double r2462540 = y;
        double r2462541 = z;
        double r2462542 = log(r2462541);
        double r2462543 = r2462540 * r2462542;
        double r2462544 = t;
        double r2462545 = 1.0;
        double r2462546 = r2462544 - r2462545;
        double r2462547 = a;
        double r2462548 = log(r2462547);
        double r2462549 = r2462546 * r2462548;
        double r2462550 = r2462543 + r2462549;
        double r2462551 = b;
        double r2462552 = r2462550 - r2462551;
        double r2462553 = exp(r2462552);
        double r2462554 = r2462539 * r2462553;
        double r2462555 = r2462554 / r2462540;
        return r2462555;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r2462556 = 1.0;
        double r2462557 = 1.0;
        double r2462558 = a;
        double r2462559 = r2462557 / r2462558;
        double r2462560 = cbrt(r2462559);
        double r2462561 = r2462560 * r2462560;
        double r2462562 = log(r2462561);
        double r2462563 = r2462556 * r2462562;
        double r2462564 = exp(r2462563);
        double r2462565 = -0.3333333333333333;
        double r2462566 = pow(r2462558, r2462565);
        double r2462567 = log(r2462566);
        double r2462568 = r2462556 * r2462567;
        double r2462569 = t;
        double r2462570 = log(r2462559);
        double r2462571 = r2462569 * r2462570;
        double r2462572 = b;
        double r2462573 = r2462571 + r2462572;
        double r2462574 = z;
        double r2462575 = r2462557 / r2462574;
        double r2462576 = log(r2462575);
        double r2462577 = y;
        double r2462578 = r2462576 * r2462577;
        double r2462579 = r2462573 + r2462578;
        double r2462580 = r2462568 - r2462579;
        double r2462581 = exp(r2462580);
        double r2462582 = r2462564 * r2462581;
        double r2462583 = x;
        double r2462584 = r2462582 * r2462583;
        double r2462585 = r2462584 / r2462577;
        double r2462586 = cbrt(r2462585);
        double r2462587 = r2462586 * r2462586;
        double r2462588 = r2462586 * r2462587;
        return r2462588;
}

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 1.8

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

  2. Taylor expanded around inf 1.8

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

  4. Applied add-cube-cbrt1.9

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

  5. Applied log-prod1.9

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

  6. Applied distribute-lft-in1.9

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

  7. Applied associate--l+1.9

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

  8. Applied exp-sum1.8

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

  9. Taylor expanded around 0 1.8

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

  11. Applied add-cube-cbrt1.8

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

  12. Final simplification1.8

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

Reproduce

herbie shell --seed 2019130 
(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))