Error

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Derivation

1. Split input into 2 regimes

2. if b < -3.305859051545688e-74 or 1.0250610450472451e-16 < b

   1. Initial program 0.6

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

   3. Applied *-un-lft-identity0.6

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

   4. Applied exp-prod0.6

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

   5. Simplified0.6

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

   7. Applied add-cbrt-cube1.8

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

   if -3.305859051545688e-74 < b < 1.0250610450472451e-16

   1. Initial program 3.4

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

   3. Applied exp-diff3.4

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

   4. Simplified9.2

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

   6. Applied pow-sub9.1

      \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{{a}^{t}}{{a}^{1.0}}} \cdot {z}^{y}}{e^{b}}}{y}\]

   7. Applied associate-*l/9.1

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

4. Final simplification5.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.305859051545688 \cdot 10^{-74} \lor \neg \left(b \le 1.0250610450472451 \cdot 10^{-16}\right):\\ \;\;\;\;\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y} \cdot \left(\frac{x \cdot {e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y} \cdot \frac{x \cdot {e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{a}^{t} \cdot {z}^{y}}{{a}^{1.0}}}{e^{b}}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2018360 
(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

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