Average Error: 2.0 → 2.1
Time: 1.7m
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 r236914 = x;
        double r236915 = y;
        double r236916 = z;
        double r236917 = log(r236916);
        double r236918 = r236915 * r236917;
        double r236919 = t;
        double r236920 = 1.0;
        double r236921 = r236919 - r236920;
        double r236922 = a;
        double r236923 = log(r236922);
        double r236924 = r236921 * r236923;
        double r236925 = r236918 + r236924;
        double r236926 = b;
        double r236927 = r236925 - r236926;
        double r236928 = exp(r236927);
        double r236929 = r236914 * r236928;
        double r236930 = r236929 / r236915;
        return r236930;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r236931 = x;
        double r236932 = z;
        double r236933 = log(r236932);
        double r236934 = y;
        double r236935 = r236933 * r236934;
        double r236936 = b;
        double r236937 = a;
        double r236938 = log(r236937);
        double r236939 = t;
        double r236940 = 1.0;
        double r236941 = r236939 - r236940;
        double r236942 = r236938 * r236941;
        double r236943 = r236936 - r236942;
        double r236944 = r236935 - r236943;
        double r236945 = exp(r236944);
        double r236946 = r236945 / r236934;
        double r236947 = r236931 * r236946;
        return r236947;
}

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))