Average Error: 2.0 → 2.1
Time: 1.8m
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[x \cdot \frac{e^{\log z \cdot y - \left(b - \log a \cdot \left(t - 1\right)\right)}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
x \cdot \frac{e^{\log z \cdot y - \left(b - \log a \cdot \left(t - 1\right)\right)}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r237908 = x;
        double r237909 = y;
        double r237910 = z;
        double r237911 = log(r237910);
        double r237912 = r237909 * r237911;
        double r237913 = t;
        double r237914 = 1.0;
        double r237915 = r237913 - r237914;
        double r237916 = a;
        double r237917 = log(r237916);
        double r237918 = r237915 * r237917;
        double r237919 = r237912 + r237918;
        double r237920 = b;
        double r237921 = r237919 - r237920;
        double r237922 = exp(r237921);
        double r237923 = r237908 * r237922;
        double r237924 = r237923 / r237909;
        return r237924;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r237925 = x;
        double r237926 = z;
        double r237927 = log(r237926);
        double r237928 = y;
        double r237929 = r237927 * r237928;
        double r237930 = b;
        double r237931 = a;
        double r237932 = log(r237931);
        double r237933 = t;
        double r237934 = 1.0;
        double r237935 = r237933 - r237934;
        double r237936 = r237932 * r237935;
        double r237937 = r237930 - r237936;
        double r237938 = r237929 - r237937;
        double r237939 = exp(r237938);
        double r237940 = r237939 / r237928;
        double r237941 = r237925 * r237940;
        return r237941;
}

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. Using strategy rm

  3. Applied *-un-lft-identity2.0

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

  4. Applied times-frac2.1

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

  5. Simplified2.1

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

  6. Simplified18.2

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

  8. Applied add-exp-log18.9

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

  9. Applied pow-exp18.9

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

  10. Applied div-exp13.4

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

  11. Applied add-exp-log13.4

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

  12. Applied pow-exp13.4

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

  13. Applied div-exp2.1

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

  14. Final simplification2.1

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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))