Average Error: 1.8 → 1.0
Time: 34.8s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{{e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{{e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}}
double f(double x, double y, double z, double t, double a, double b) {
        double r1567541 = x;
        double r1567542 = y;
        double r1567543 = z;
        double r1567544 = log(r1567543);
        double r1567545 = r1567542 * r1567544;
        double r1567546 = t;
        double r1567547 = 1.0;
        double r1567548 = r1567546 - r1567547;
        double r1567549 = a;
        double r1567550 = log(r1567549);
        double r1567551 = r1567548 * r1567550;
        double r1567552 = r1567545 + r1567551;
        double r1567553 = b;
        double r1567554 = r1567552 - r1567553;
        double r1567555 = exp(r1567554);
        double r1567556 = r1567541 * r1567555;
        double r1567557 = r1567556 / r1567542;
        return r1567557;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1567558 = x;
        double r1567559 = cbrt(r1567558);
        double r1567560 = r1567559 * r1567559;
        double r1567561 = y;
        double r1567562 = cbrt(r1567561);
        double r1567563 = r1567562 * r1567562;
        double r1567564 = z;
        double r1567565 = log(r1567564);
        double r1567566 = r1567561 * r1567565;
        double r1567567 = t;
        double r1567568 = 1.0;
        double r1567569 = r1567567 - r1567568;
        double r1567570 = a;
        double r1567571 = log(r1567570);
        double r1567572 = r1567569 * r1567571;
        double r1567573 = r1567566 + r1567572;
        double r1567574 = b;
        double r1567575 = r1567573 - r1567574;
        double r1567576 = exp(r1567575);
        double r1567577 = cbrt(r1567576);
        double r1567578 = r1567577 * r1567577;
        double r1567579 = r1567563 / r1567578;
        double r1567580 = r1567560 / r1567579;
        double r1567581 = cbrt(r1567562);
        double r1567582 = cbrt(r1567563);
        double r1567583 = r1567581 * r1567582;
        double r1567584 = exp(1.0);
        double r1567585 = pow(r1567584, r1567575);
        double r1567586 = cbrt(r1567585);
        double r1567587 = r1567583 / r1567586;
        double r1567588 = r1567559 / r1567587;
        double r1567589 = r1567580 * r1567588;
        return r1567589;
}

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. Using strategy rm

  3. Applied associate-/l*1.9

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

  5. Applied add-cube-cbrt1.9

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

  6. Applied add-cube-cbrt1.9

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

  7. Applied times-frac1.9

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

  8. Applied add-cube-cbrt1.9

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

  9. Applied times-frac1.0

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

  11. Applied *-un-lft-identity1.0

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

  12. Applied exp-prod1.0

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

  13. Simplified1.0

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

  15. Applied add-cube-cbrt1.0

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

  16. Applied cbrt-prod1.0

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

  17. Final simplification1.0

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

Reproduce

herbie shell --seed 2019156 
(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))