Average Error: 2.0 → 0.7
Time: 16.0s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(\left(x \cdot \frac{{\left(\sqrt{\frac{1}{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \frac{\frac{\sqrt[3]{{\left(\sqrt{\frac{1}{a}}\right)}^{1}} \cdot \sqrt[3]{{\left(\sqrt{\frac{1}{a}}\right)}^{1}}}{\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\frac{\sqrt[3]{{\left(\sqrt{\frac{1}{a}}\right)}^{1}}}{\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\sqrt[3]{y}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\left(\left(x \cdot \frac{{\left(\sqrt{\frac{1}{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \frac{\frac{\sqrt[3]{{\left(\sqrt{\frac{1}{a}}\right)}^{1}} \cdot \sqrt[3]{{\left(\sqrt{\frac{1}{a}}\right)}^{1}}}{\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}} \cdot \sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\frac{\sqrt[3]{{\left(\sqrt{\frac{1}{a}}\right)}^{1}}}{\sqrt[3]{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}{\sqrt[3]{y}}
double f(double x, double y, double z, double t, double a, double b) {
        double r94965 = x;
        double r94966 = y;
        double r94967 = z;
        double r94968 = log(r94967);
        double r94969 = r94966 * r94968;
        double r94970 = t;
        double r94971 = 1.0;
        double r94972 = r94970 - r94971;
        double r94973 = a;
        double r94974 = log(r94973);
        double r94975 = r94972 * r94974;
        double r94976 = r94969 + r94975;
        double r94977 = b;
        double r94978 = r94976 - r94977;
        double r94979 = exp(r94978);
        double r94980 = r94965 * r94979;
        double r94981 = r94980 / r94966;
        return r94981;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r94982 = x;
        double r94983 = 1.0;
        double r94984 = a;
        double r94985 = r94983 / r94984;
        double r94986 = sqrt(r94985);
        double r94987 = 1.0;
        double r94988 = pow(r94986, r94987);
        double r94989 = y;
        double r94990 = z;
        double r94991 = r94983 / r94990;
        double r94992 = log(r94991);
        double r94993 = r94989 * r94992;
        double r94994 = log(r94985);
        double r94995 = t;
        double r94996 = r94994 * r94995;
        double r94997 = b;
        double r94998 = r94996 + r94997;
        double r94999 = r94993 + r94998;
        double r95000 = exp(r94999);
        double r95001 = sqrt(r95000);
        double r95002 = r94988 / r95001;
        double r95003 = r94982 * r95002;
        double r95004 = cbrt(r94988);
        double r95005 = r95004 * r95004;
        double r95006 = cbrt(r95001);
        double r95007 = r95006 * r95006;
        double r95008 = r95005 / r95007;
        double r95009 = cbrt(r94989);
        double r95010 = r95009 * r95009;
        double r95011 = r95008 / r95010;
        double r95012 = r95003 * r95011;
        double r95013 = r95004 / r95006;
        double r95014 = r95013 / r95009;
        double r95015 = r95012 * r95014;
        return r95015;
}

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

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

  5. Applied add-sqr-sqrt1.3

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

  6. Applied add-sqr-sqrt1.3

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

  7. Applied unpow-prod-down1.3

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

  8. Applied times-frac1.3

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

  9. Applied associate-*r*1.3

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

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

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

  12. Applied times-frac1.1

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

  13. Simplified1.1

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

  15. Applied add-cube-cbrt1.3

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

  16. Applied add-cube-cbrt1.3

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

  17. Applied add-cube-cbrt1.3

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

  18. Applied times-frac1.3

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

  19. Applied times-frac1.3

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

  20. Applied associate-*r*0.7

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

  21. Final simplification0.7

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

Reproduce

herbie shell --seed 2020060 
(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))