Error

Derivation

1. Split input into 2 regimes

2. if y < -1.4424902966070684e-39 or -1.802008489021528e-303 < y

   1. Initial program 1.4

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

   3. Applied associate-/l*1.4

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

   if -1.4424902966070684e-39 < y < -1.802008489021528e-303

   1. Initial program 4.1

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

   3. Applied associate-/l*3.6

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

   4. Taylor expanded around inf 3.7

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

   5. Simplified2.2

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

   7. Applied pow-neg2.2

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

   8. Applied associate-*l/2.2

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

   9. Applied associate-*l/2.2

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

   10. Applied associate-/r/2.2

       \[\leadsto \frac{x}{\color{blue}{\frac{y}{\left(1 \cdot {z}^{y}\right) \cdot e^{(t \cdot \left(\log a\right) + \left(-b\right))_*}} \cdot {a}^{1.0}}}\]
   11. Using strategy rm

   12. Applied associate-/r*3.3

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

4. Final simplification1.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.4424902966070684 \cdot 10^{-39} \lor \neg \left(y \le -1.802008489021528 \cdot 10^{-303}\right):\\ \;\;\;\;\frac{x}{\frac{y}{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{{z}^{y} \cdot e^{(t \cdot \left(\log a\right) + \left(-b\right))_*}}}}{{a}^{1.0}}\\ \end{array}\]

Reproduce

herbie shell --seed 2018365 +o rules:numerics
(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: 30.2s)Debug log