Average Error: 2.0 → 0.5
Time: 19.6s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le 2.031077836212711156393861827249665598026 \cdot 10^{-178}:\\ \;\;\;\;{\left(\frac{1}{{a}^{1}}\right)}^{1} \cdot \frac{x}{e^{\log \left(\frac{1}{z}\right) \cdot y + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y} \cdot x\\ \end{array}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\begin{array}{l}
\mathbf{if}\;a \le 2.031077836212711156393861827249665598026 \cdot 10^{-178}:\\
\;\;\;\;{\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}\\

\mathbf{else}:\\
\;\;\;\;\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)}}}{y} \cdot x\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r105492 = x;
        double r105493 = y;
        double r105494 = z;
        double r105495 = log(r105494);
        double r105496 = r105493 * r105495;
        double r105497 = t;
        double r105498 = 1.0;
        double r105499 = r105497 - r105498;
        double r105500 = a;
        double r105501 = log(r105500);
        double r105502 = r105499 * r105501;
        double r105503 = r105496 + r105502;
        double r105504 = b;
        double r105505 = r105503 - r105504;
        double r105506 = exp(r105505);
        double r105507 = r105492 * r105506;
        double r105508 = r105507 / r105493;
        return r105508;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r105509 = a;
        double r105510 = 2.0310778362127112e-178;
        bool r105511 = r105509 <= r105510;
        double r105512 = 1.0;
        double r105513 = 1.0;
        double r105514 = pow(r105509, r105513);
        double r105515 = r105512 / r105514;
        double r105516 = pow(r105515, r105513);
        double r105517 = x;
        double r105518 = z;
        double r105519 = r105512 / r105518;
        double r105520 = log(r105519);
        double r105521 = y;
        double r105522 = r105520 * r105521;
        double r105523 = r105512 / r105509;
        double r105524 = log(r105523);
        double r105525 = t;
        double r105526 = r105524 * r105525;
        double r105527 = b;
        double r105528 = r105526 + r105527;
        double r105529 = r105522 + r105528;
        double r105530 = exp(r105529);
        double r105531 = r105530 * r105521;
        double r105532 = r105517 / r105531;
        double r105533 = r105516 * r105532;
        double r105534 = pow(r105523, r105513);
        double r105535 = r105521 * r105520;
        double r105536 = r105535 + r105528;
        double r105537 = exp(r105536);
        double r105538 = r105534 / r105537;
        double r105539 = r105538 / r105521;
        double r105540 = r105539 * r105517;
        double r105541 = r105511 ? r105533 : r105540;
        return r105541;
}

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 a < 2.0310778362127112e-178

    1. Initial program 0.7

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

    2. Taylor expanded around inf 0.7

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

    3. Simplified5.7

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

    4. Taylor expanded around inf 0.1

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

    if 2.0310778362127112e-178 < a

    1. Initial program 2.3

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

    2. Taylor expanded around inf 2.4

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

    3. Simplified6.4

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

    5. Applied associate-/r/0.7

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le 2.031077836212711156393861827249665598026 \cdot 10^{-178}:\\ \;\;\;\;{\left(\frac{1}{{a}^{1}}\right)}^{1} \cdot \frac{x}{e^{\log \left(\frac{1}{z}\right) \cdot y + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019352 
(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))