Average Error: 2.0 → 2.0
Time: 1.0m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{e^{(y \cdot \left(\log z\right) + \left(\left(t - 1.0\right) \cdot \log a\right))_* - b} \cdot x}{y}\]

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

Derivation

  1. Initial program 2.0

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

  2. Taylor expanded around 0 2.0

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

  3. Simplified2.0

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

  4. Final simplification2.0

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

Runtime

Time bar (total: 1.0m)Debug logProfile

herbie shell --seed 2018249 +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))