Average Error: 2.0 → 23.0
Time: 34.4s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{{\left(\frac{1}{{a}^{1}}\right)}^{1}}{\frac{e^{b}}{{z}^{y}}} \cdot \frac{\frac{x}{y}}{{\left(\frac{1}{a}\right)}^{t}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{{\left(\frac{1}{{a}^{1}}\right)}^{1}}{\frac{e^{b}}{{z}^{y}}} \cdot \frac{\frac{x}{y}}{{\left(\frac{1}{a}\right)}^{t}}
double f(double x, double y, double z, double t, double a, double b) {
        double r83335 = x;
        double r83336 = y;
        double r83337 = z;
        double r83338 = log(r83337);
        double r83339 = r83336 * r83338;
        double r83340 = t;
        double r83341 = 1.0;
        double r83342 = r83340 - r83341;
        double r83343 = a;
        double r83344 = log(r83343);
        double r83345 = r83342 * r83344;
        double r83346 = r83339 + r83345;
        double r83347 = b;
        double r83348 = r83346 - r83347;
        double r83349 = exp(r83348);
        double r83350 = r83335 * r83349;
        double r83351 = r83350 / r83336;
        return r83351;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r83352 = 1.0;
        double r83353 = a;
        double r83354 = 1.0;
        double r83355 = pow(r83353, r83354);
        double r83356 = r83352 / r83355;
        double r83357 = pow(r83356, r83354);
        double r83358 = b;
        double r83359 = exp(r83358);
        double r83360 = z;
        double r83361 = y;
        double r83362 = pow(r83360, r83361);
        double r83363 = r83359 / r83362;
        double r83364 = r83357 / r83363;
        double r83365 = x;
        double r83366 = r83365 / r83361;
        double r83367 = r83352 / r83353;
        double r83368 = t;
        double r83369 = pow(r83367, r83368);
        double r83370 = r83366 / r83369;
        double r83371 = r83364 * r83370;
        return r83371;
}

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 add-cube-cbrt2.0

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

  4. Taylor expanded around inf 2.0

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

  5. Simplified6.6

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

  6. Taylor expanded around inf 1.5

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

  7. Final simplification23.0

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

Reproduce

herbie shell --seed 2019308 
(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))