Average Error: 2.1 → 2.1
Time: 55.2s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot \left(\left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{{\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)} \cdot {\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)}}\right)}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot \left(\left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{{\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)} \cdot {\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)}}\right)}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r4627110 = x;
        double r4627111 = y;
        double r4627112 = z;
        double r4627113 = log(r4627112);
        double r4627114 = r4627111 * r4627113;
        double r4627115 = t;
        double r4627116 = 1.0;
        double r4627117 = r4627115 - r4627116;
        double r4627118 = a;
        double r4627119 = log(r4627118);
        double r4627120 = r4627117 * r4627119;
        double r4627121 = r4627114 + r4627120;
        double r4627122 = b;
        double r4627123 = r4627121 - r4627122;
        double r4627124 = exp(r4627123);
        double r4627125 = r4627110 * r4627124;
        double r4627126 = r4627125 / r4627111;
        return r4627126;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r4627127 = x;
        double r4627128 = a;
        double r4627129 = log(r4627128);
        double r4627130 = t;
        double r4627131 = 1.0;
        double r4627132 = r4627130 - r4627131;
        double r4627133 = r4627129 * r4627132;
        double r4627134 = z;
        double r4627135 = log(r4627134);
        double r4627136 = y;
        double r4627137 = r4627135 * r4627136;
        double r4627138 = r4627133 + r4627137;
        double r4627139 = b;
        double r4627140 = r4627138 - r4627139;
        double r4627141 = exp(r4627140);
        double r4627142 = cbrt(r4627141);
        double r4627143 = r4627142 * r4627142;
        double r4627144 = exp(1.0);
        double r4627145 = sqrt(r4627144);
        double r4627146 = pow(r4627145, r4627140);
        double r4627147 = r4627146 * r4627146;
        double r4627148 = cbrt(r4627147);
        double r4627149 = r4627143 * r4627148;
        double r4627150 = r4627127 * r4627149;
        double r4627151 = r4627150 / r4627136;
        return r4627151;
}

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 2.1

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

  3. Applied add-cube-cbrt2.1

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

  5. Applied *-un-lft-identity2.1

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

  6. Applied *-un-lft-identity2.1

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

  7. Applied distribute-lft-out--2.1

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

  8. Applied exp-prod2.1

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

  9. Simplified2.1

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

  11. Applied add-sqr-sqrt2.2

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

  12. Applied unpow-prod-down2.1

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

  13. Final simplification2.1

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

Reproduce

herbie shell --seed 2019149 +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))