Average Error: 1.9 → 1.9
Time: 5.0m
Precision: 64
Internal Precision: 384
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot e^{\log a \cdot \left(t - 1.0\right) - \left(b - \log z \cdot y\right)}}{y}\]

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 1.9

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

  2. Applied simplify22.2

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

  4. Applied associate-*l/17.6

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

  6. Applied pow-to-exp17.6

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

  7. Applied div-exp12.4

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

  8. Applied pow-to-exp13.1

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

  9. Applied div-exp1.9

    \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - \left(b - \log z \cdot y\right)}}}{y}\]
  10. Removed slow pow expressions.

Runtime

Time bar (total: 5.0m)Debug logProfile

herbie shell --seed '#(1063185673 2139736501 2393378123 1907444849 1070993796 1007244912)' 
(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))