Error

Derivation

1. Split input into 2 regimes

2. if y < -5030318244.573108 or 6.369805194853656e-15 < y

   1. Initial program 0.1

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

   3. Applied associate-/l*0.1

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

   if -5030318244.573108 < y < 6.369805194853656e-15

   1. Initial program 3.7

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

   2. Taylor expanded around inf 3.7

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

   3. Simplified2.7

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

   5. Applied pow-neg2.7

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

   6. Applied associate-*l/2.7

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

   7. Applied associate-*l/2.6

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

   8. Applied associate-*r/2.6

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

4. Final simplification1.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5030318244.573108 \lor \neg \left(y \le 6.369805194853656 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{\frac{y}{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left({z}^{y} \cdot e^{(t \cdot \left(\log a\right) + \left(-b\right))_*}\right)}{{a}^{1.0}}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019002 +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: 44.9s)Debug log