Average Error: 2.1 → 1.9
Time: 35.3s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \le -702.6583505807568599266232922673225402832 \lor \neg \left(\left(t - 1\right) \cdot \log a \le -106.4073004455099749065993819385766983032\right):\\ \;\;\;\;\frac{x \cdot e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log \left({z}^{y}\right) + t \cdot \log a}}{y \cdot \left(a \cdot e^{b}\right)} \cdot x\\ \end{array}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\begin{array}{l}
\mathbf{if}\;\left(t - 1\right) \cdot \log a \le -702.6583505807568599266232922673225402832 \lor \neg \left(\left(t - 1\right) \cdot \log a \le -106.4073004455099749065993819385766983032\right):\\
\;\;\;\;\frac{x \cdot e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b}}{y}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r58913 = x;
        double r58914 = y;
        double r58915 = z;
        double r58916 = log(r58915);
        double r58917 = r58914 * r58916;
        double r58918 = t;
        double r58919 = 1.0;
        double r58920 = r58918 - r58919;
        double r58921 = a;
        double r58922 = log(r58921);
        double r58923 = r58920 * r58922;
        double r58924 = r58917 + r58923;
        double r58925 = b;
        double r58926 = r58924 - r58925;
        double r58927 = exp(r58926);
        double r58928 = r58913 * r58927;
        double r58929 = r58928 / r58914;
        return r58929;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r58930 = t;
        double r58931 = 1.0;
        double r58932 = r58930 - r58931;
        double r58933 = a;
        double r58934 = log(r58933);
        double r58935 = r58932 * r58934;
        double r58936 = -702.6583505807569;
        bool r58937 = r58935 <= r58936;
        double r58938 = -106.40730044550997;
        bool r58939 = r58935 <= r58938;
        double r58940 = !r58939;
        bool r58941 = r58937 || r58940;
        double r58942 = x;
        double r58943 = z;
        double r58944 = log(r58943);
        double r58945 = y;
        double r58946 = r58944 * r58945;
        double r58947 = r58935 + r58946;
        double r58948 = b;
        double r58949 = r58947 - r58948;
        double r58950 = exp(r58949);
        double r58951 = r58942 * r58950;
        double r58952 = r58951 / r58945;
        double r58953 = pow(r58943, r58945);
        double r58954 = log(r58953);
        double r58955 = r58930 * r58934;
        double r58956 = r58954 + r58955;
        double r58957 = exp(r58956);
        double r58958 = exp(r58948);
        double r58959 = r58933 * r58958;
        double r58960 = r58945 * r58959;
        double r58961 = r58957 / r58960;
        double r58962 = r58961 * r58942;
        double r58963 = r58941 ? r58952 : r58962;
        return r58963;
}

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 2 regimes

  2. if (* (- t 1.0) (log a)) < -702.6583505807569 or -106.40730044550997 < (* (- t 1.0) (log a))

    1. Initial program 0.6

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

    if -702.6583505807569 < (* (- t 1.0) (log a)) < -106.40730044550997

    1. Initial program 6.9

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

    3. Applied associate-/l*2.3

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

    4. Simplified6.1

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

    6. Applied *-un-lft-identity6.1

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

    7. Applied sub-neg6.1

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

    8. Applied unpow-prod-up6.0

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

    9. Applied times-frac6.0

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

    10. Applied associate-*r*6.0

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

    11. Simplified6.0

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

    13. Applied div-inv6.0

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

    14. Simplified6.0

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

    15. Taylor expanded around inf 6.0

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

    16. Simplified6.0

      \[\leadsto x \cdot \color{blue}{\frac{e^{-\left(\left(-\log \left({z}^{y}\right)\right) + \left(-\log a \cdot t\right)\right)}}{y \cdot \left(e^{b} \cdot a\right)}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \le -702.6583505807568599266232922673225402832 \lor \neg \left(\left(t - 1\right) \cdot \log a \le -106.4073004455099749065993819385766983032\right):\\ \;\;\;\;\frac{x \cdot e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log \left({z}^{y}\right) + t \cdot \log a}}{y \cdot \left(a \cdot e^{b}\right)} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(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))