Average Error: 1.8 → 1.8
Time: 37.9s
Precision: 64
Internal Precision: 128
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
\[\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}\]

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. Initial program 1.8

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  2. Taylor expanded around -inf 62.9

    \[\leadsto \frac{x \cdot e^{\left(\color{blue}{\left(\log -1 - \log \left(\frac{-1}{z}\right)\right) \cdot y} + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  3. Simplified1.8

    \[\leadsto \frac{x \cdot e^{\left(\color{blue}{\log z \cdot y} + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  4. Final simplification1.8

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

Reproduce

herbie shell --seed 2019026 
(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))