Error

Try it out

Derivation

1. Split input into 2 regimes

2. if y < -4.3882314950956804e-250 or -3.9719064524468603e-283 < y

   1. Initial program 1.9

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

   3. Applied *-un-lft-identity1.9

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

   4. Applied exp-prod2.0

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

   5. Simplified2.0

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

   if -4.3882314950956804e-250 < y < -3.9719064524468603e-283

   1. Initial program 5.0

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

   3. Applied *-un-lft-identity5.0

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

   4. Applied exp-prod5.1

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

   5. Simplified5.1

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

   6. Taylor expanded around inf 5.0

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

   7. Simplified10.2

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

   9. Applied associate-/l*10.1

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

   11. Applied clear-num10.1

       \[\leadsto \color{blue}{\frac{1}{\frac{\frac{y}{\left({z}^{y} \cdot e^{-b}\right) \cdot \left({a}^{t} \cdot {a}^{\left(-1.0\right)}\right)}}{x}}}\]
3. Recombined 2 regimes into one program.

4. Final simplification2.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.3882314950956804 \cdot 10^{-250} \lor \neg \left(y \le -3.9719064524468603 \cdot 10^{-283}\right):\\ \;\;\;\;\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y}{\left(e^{-b} \cdot {z}^{y}\right) \cdot \left({a}^{\left(-1.0\right)} \cdot {a}^{t}\right)}}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019005 
(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))

Details

Time bar (total: 44.7s)Debug log