Average Error: 2.1 → 1.7
Time: 1.3m
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.3784794480955156 \cdot 10^{+209}:\\ \;\;\;\;\frac{\left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}} \cdot \sqrt{{\left(e^{\sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b} \cdot \sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}\right)}^{\left(\sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}\right)}}\right) \cdot x}{y}\\ \mathbf{elif}\;x \le 5.310858125257187 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{\sqrt[3]{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b\right)}}{y}\\ \end{array}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.3784794480955156 \cdot 10^{+209}:\\
\;\;\;\;\frac{\left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}} \cdot \sqrt{{\left(e^{\sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b} \cdot \sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}\right)}^{\left(\sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}\right)}}\right) \cdot x}{y}\\

\mathbf{elif}\;x \le 5.310858125257187 \cdot 10^{+20}:\\
\;\;\;\;\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{\sqrt[3]{y}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b\right)}}{y}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r3252952 = x;
        double r3252953 = y;
        double r3252954 = z;
        double r3252955 = log(r3252954);
        double r3252956 = r3252953 * r3252955;
        double r3252957 = t;
        double r3252958 = 1.0;
        double r3252959 = r3252957 - r3252958;
        double r3252960 = a;
        double r3252961 = log(r3252960);
        double r3252962 = r3252959 * r3252961;
        double r3252963 = r3252956 + r3252962;
        double r3252964 = b;
        double r3252965 = r3252963 - r3252964;
        double r3252966 = exp(r3252965);
        double r3252967 = r3252952 * r3252966;
        double r3252968 = r3252967 / r3252953;
        return r3252968;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3252969 = x;
        double r3252970 = -1.3784794480955156e+209;
        bool r3252971 = r3252969 <= r3252970;
        double r3252972 = a;
        double r3252973 = log(r3252972);
        double r3252974 = t;
        double r3252975 = 1.0;
        double r3252976 = r3252974 - r3252975;
        double r3252977 = r3252973 * r3252976;
        double r3252978 = y;
        double r3252979 = z;
        double r3252980 = log(r3252979);
        double r3252981 = r3252978 * r3252980;
        double r3252982 = r3252977 + r3252981;
        double r3252983 = b;
        double r3252984 = r3252982 - r3252983;
        double r3252985 = exp(r3252984);
        double r3252986 = sqrt(r3252985);
        double r3252987 = cbrt(r3252984);
        double r3252988 = r3252987 * r3252987;
        double r3252989 = exp(r3252988);
        double r3252990 = pow(r3252989, r3252987);
        double r3252991 = sqrt(r3252990);
        double r3252992 = r3252986 * r3252991;
        double r3252993 = r3252992 * r3252969;
        double r3252994 = r3252993 / r3252978;
        double r3252995 = 5.310858125257187e+20;
        bool r3252996 = r3252969 <= r3252995;
        double r3252997 = cbrt(r3252978);
        double r3252998 = r3252997 * r3252997;
        double r3252999 = r3252969 / r3252998;
        double r3253000 = r3252985 / r3252997;
        double r3253001 = r3252999 * r3253000;
        double r3253002 = exp(1.0);
        double r3253003 = pow(r3253002, r3252984);
        double r3253004 = r3252969 * r3253003;
        double r3253005 = r3253004 / r3252978;
        double r3253006 = r3252996 ? r3253001 : r3253005;
        double r3253007 = r3252971 ? r3252994 : r3253006;
        return r3253007;
}

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. Split input into 3 regimes

  2. if x < -1.3784794480955156e+209

    1. Initial program 0.6

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

    3. Applied add-sqr-sqrt0.6

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

    5. Applied add-cube-cbrt0.7

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

    6. Applied exp-prod0.7

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

    if -1.3784794480955156e+209 < x < 5.310858125257187e+20

    1. Initial program 2.7

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

    3. Applied add-cube-cbrt2.7

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

    4. Applied times-frac2.1

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

    if 5.310858125257187e+20 < x

    1. Initial program 0.7

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

    3. Applied *-un-lft-identity0.7

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

    4. Applied exp-prod0.8

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

    5. Simplified0.8

      \[\leadsto \frac{x \cdot {\color{blue}{e}}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.3784794480955156 \cdot 10^{+209}:\\ \;\;\;\;\frac{\left(\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}} \cdot \sqrt{{\left(e^{\sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b} \cdot \sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}\right)}^{\left(\sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}\right)}}\right) \cdot x}{y}\\ \mathbf{elif}\;x \le 5.310858125257187 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{\sqrt[3]{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b\right)}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019143 
(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))