Average Error: 2.0 → 1.3
Time: 36.6s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\frac{{a}^{\left(-1\right)}}{\sqrt{e^{b + \left(-\left(\log a \cdot t + \log z \cdot y\right)\right)}}} \cdot \frac{x}{\sqrt{e^{\left(b - \log a \cdot t\right) - \log z \cdot y}}}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{\frac{{a}^{\left(-1\right)}}{\sqrt{e^{b + \left(-\left(\log a \cdot t + \log z \cdot y\right)\right)}}} \cdot \frac{x}{\sqrt{e^{\left(b - \log a \cdot t\right) - \log z \cdot y}}}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r50856 = x;
        double r50857 = y;
        double r50858 = z;
        double r50859 = log(r50858);
        double r50860 = r50857 * r50859;
        double r50861 = t;
        double r50862 = 1.0;
        double r50863 = r50861 - r50862;
        double r50864 = a;
        double r50865 = log(r50864);
        double r50866 = r50863 * r50865;
        double r50867 = r50860 + r50866;
        double r50868 = b;
        double r50869 = r50867 - r50868;
        double r50870 = exp(r50869);
        double r50871 = r50856 * r50870;
        double r50872 = r50871 / r50857;
        return r50872;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r50873 = a;
        double r50874 = 1.0;
        double r50875 = -r50874;
        double r50876 = pow(r50873, r50875);
        double r50877 = b;
        double r50878 = log(r50873);
        double r50879 = t;
        double r50880 = r50878 * r50879;
        double r50881 = z;
        double r50882 = log(r50881);
        double r50883 = y;
        double r50884 = r50882 * r50883;
        double r50885 = r50880 + r50884;
        double r50886 = -r50885;
        double r50887 = r50877 + r50886;
        double r50888 = exp(r50887);
        double r50889 = sqrt(r50888);
        double r50890 = r50876 / r50889;
        double r50891 = x;
        double r50892 = r50877 - r50880;
        double r50893 = r50892 - r50884;
        double r50894 = exp(r50893);
        double r50895 = sqrt(r50894);
        double r50896 = r50891 / r50895;
        double r50897 = r50890 * r50896;
        double r50898 = r50897 / r50883;
        return r50898;
}

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 2.0

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

  2. Taylor expanded around inf 2.0

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

  3. Simplified1.3

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

  5. Applied add-sqr-sqrt1.3

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

  6. Applied *-un-lft-identity1.3

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

  7. Applied unpow-prod-down1.3

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

  8. Applied times-frac1.3

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

  9. Applied associate-*r*1.3

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

  10. Simplified1.3

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

  11. Final simplification1.3

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

Reproduce

herbie shell --seed 2019305 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))