Average Error: 2.0 → 1.1
Time: 52.4s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.9895651398403923 \cdot 10^{-156}:\\ \;\;\;\;\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{y}}\right)\\ \mathbf{elif}\;x \le 9.113064666277571 \cdot 10^{+23}:\\ \;\;\;\;e^{\left(\log a \cdot \left(t - 1.0\right) - b\right) + y \cdot \log z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{y}}\right)\\ \end{array}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.9895651398403923 \cdot 10^{-156}:\\
\;\;\;\;\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{y}}\right)\\

\mathbf{elif}\;x \le 9.113064666277571 \cdot 10^{+23}:\\
\;\;\;\;e^{\left(\log a \cdot \left(t - 1.0\right) - b\right) + y \cdot \log z} \cdot \frac{x}{y}\\

\mathbf{else}:\\
\;\;\;\;\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{y}}\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r3706377 = x;
        double r3706378 = y;
        double r3706379 = z;
        double r3706380 = log(r3706379);
        double r3706381 = r3706378 * r3706380;
        double r3706382 = t;
        double r3706383 = 1.0;
        double r3706384 = r3706382 - r3706383;
        double r3706385 = a;
        double r3706386 = log(r3706385);
        double r3706387 = r3706384 * r3706386;
        double r3706388 = r3706381 + r3706387;
        double r3706389 = b;
        double r3706390 = r3706388 - r3706389;
        double r3706391 = exp(r3706390);
        double r3706392 = r3706377 * r3706391;
        double r3706393 = r3706392 / r3706378;
        return r3706393;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3706394 = x;
        double r3706395 = -1.9895651398403923e-156;
        bool r3706396 = r3706394 <= r3706395;
        double r3706397 = exp(1.0);
        double r3706398 = a;
        double r3706399 = log(r3706398);
        double r3706400 = t;
        double r3706401 = 1.0;
        double r3706402 = r3706400 - r3706401;
        double r3706403 = r3706399 * r3706402;
        double r3706404 = y;
        double r3706405 = z;
        double r3706406 = log(r3706405);
        double r3706407 = r3706404 * r3706406;
        double r3706408 = r3706403 + r3706407;
        double r3706409 = b;
        double r3706410 = r3706408 - r3706409;
        double r3706411 = pow(r3706397, r3706410);
        double r3706412 = r3706394 * r3706411;
        double r3706413 = r3706412 / r3706404;
        double r3706414 = cbrt(r3706413);
        double r3706415 = exp(r3706410);
        double r3706416 = r3706394 * r3706415;
        double r3706417 = r3706416 / r3706404;
        double r3706418 = cbrt(r3706417);
        double r3706419 = r3706418 * r3706418;
        double r3706420 = r3706414 * r3706419;
        double r3706421 = 9.113064666277571e+23;
        bool r3706422 = r3706394 <= r3706421;
        double r3706423 = r3706403 - r3706409;
        double r3706424 = r3706423 + r3706407;
        double r3706425 = exp(r3706424);
        double r3706426 = r3706394 / r3706404;
        double r3706427 = r3706425 * r3706426;
        double r3706428 = r3706422 ? r3706427 : r3706420;
        double r3706429 = r3706396 ? r3706420 : r3706428;
        return r3706429;
}

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 < -1.9895651398403923e-156 or 9.113064666277571e+23 < x

    1. Initial program 1.1

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt1.1

      \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity1.1

      \[\leadsto \left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot e^{\color{blue}{1 \cdot \left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}{y}}\]

    6. Applied exp-prod1.1

      \[\leadsto \left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot \color{blue}{{\left(e^{1}\right)}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}{y}}\]

    7. Simplified1.1

      \[\leadsto \left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot {\color{blue}{e}}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y}}\]

    if -1.9895651398403923e-156 < x < 9.113064666277571e+23

    1. Initial program 3.3

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]

    2. Taylor expanded around inf 3.3

      \[\leadsto \color{blue}{\frac{x \cdot e^{1.0 \cdot \log \left(\frac{1}{a}\right) - \left(\log \left(\frac{1}{z}\right) \cdot y + \left(b + t \cdot \log \left(\frac{1}{a}\right)\right)\right)}}{y}}\]

    3. Simplified1.1

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(\left(t - 1.0\right) \cdot \log a - b\right) + \log z \cdot y}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.9895651398403923 \cdot 10^{-156}:\\ \;\;\;\;\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{y}}\right)\\ \mathbf{elif}\;x \le 9.113064666277571 \cdot 10^{+23}:\\ \;\;\;\;e^{\left(\log a \cdot \left(t - 1.0\right) - b\right) + y \cdot \log z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}{y}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019146 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))