Average Error: 2.0 → 0.3
Time: 46.1s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -8.9526966727005439 \cdot 10^{73} \lor \neg \left(x \le 1.54253563263351339 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{1}{a}\right)}^{1} \cdot \frac{\frac{1}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\frac{y}{x}}\\ \end{array}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -8.9526966727005439 \cdot 10^{73} \lor \neg \left(x \le 1.54253563263351339 \cdot 10^{-62}\right):\\
\;\;\;\;\frac{x \cdot \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}\\

\mathbf{else}:\\
\;\;\;\;{\left(\frac{1}{a}\right)}^{1} \cdot \frac{\frac{1}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\frac{y}{x}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r212295 = x;
        double r212296 = y;
        double r212297 = z;
        double r212298 = log(r212297);
        double r212299 = r212296 * r212298;
        double r212300 = t;
        double r212301 = 1.0;
        double r212302 = r212300 - r212301;
        double r212303 = a;
        double r212304 = log(r212303);
        double r212305 = r212302 * r212304;
        double r212306 = r212299 + r212305;
        double r212307 = b;
        double r212308 = r212306 - r212307;
        double r212309 = exp(r212308);
        double r212310 = r212295 * r212309;
        double r212311 = r212310 / r212296;
        return r212311;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r212312 = x;
        double r212313 = -8.952696672700544e+73;
        bool r212314 = r212312 <= r212313;
        double r212315 = 1.5425356326335134e-62;
        bool r212316 = r212312 <= r212315;
        double r212317 = !r212316;
        bool r212318 = r212314 || r212317;
        double r212319 = 1.0;
        double r212320 = a;
        double r212321 = r212319 / r212320;
        double r212322 = 1.0;
        double r212323 = pow(r212321, r212322);
        double r212324 = y;
        double r212325 = z;
        double r212326 = r212319 / r212325;
        double r212327 = log(r212326);
        double r212328 = r212324 * r212327;
        double r212329 = log(r212321);
        double r212330 = t;
        double r212331 = r212329 * r212330;
        double r212332 = b;
        double r212333 = r212331 + r212332;
        double r212334 = r212328 + r212333;
        double r212335 = exp(r212334);
        double r212336 = r212323 / r212335;
        double r212337 = r212312 * r212336;
        double r212338 = r212337 / r212324;
        double r212339 = r212319 / r212335;
        double r212340 = r212324 / r212312;
        double r212341 = r212339 / r212340;
        double r212342 = r212323 * r212341;
        double r212343 = r212318 ? r212338 : r212342;
        return r212343;
}

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. Split input into 2 regimes

  2. if x < -8.952696672700544e+73 or 1.5425356326335134e-62 < x

    1. Initial program 0.9

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

    2. Taylor expanded around inf 0.9

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

    3. Simplified0.2

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

    if -8.952696672700544e+73 < x < 1.5425356326335134e-62

    1. Initial program 3.0

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

    2. Taylor expanded around inf 3.0

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

    3. Simplified0.4

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

    5. Applied *-un-lft-identity0.4

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

    6. Applied *-un-lft-identity0.4

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

    7. Applied times-frac0.4

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

    8. Applied div-inv0.4

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

    9. Applied times-frac0.4

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

    10. Simplified0.4

      \[\leadsto \color{blue}{{\left(\frac{1}{a}\right)}^{1}} \cdot \frac{\frac{1}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\frac{y}{x}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.9526966727005439 \cdot 10^{73} \lor \neg \left(x \le 1.54253563263351339 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{1}{a}\right)}^{1} \cdot \frac{\frac{1}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\frac{y}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 
(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))