Average Error: 1.9 → 1.3
Time: 3.7m
Precision: 64
Internal Precision: 384
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.240666482247368 \cdot 10^{+50}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1.0\right) - \left(b - \log z \cdot y\right)}}{y}\\ \mathbf{if}\;x \le 1.2788878625888583 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{y} \cdot e^{\log a \cdot \left(t - 1.0\right) - \left(b - \log z \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1.0\right) - \left(b - \log z \cdot y\right)}}{y}\\ \end{array}\]

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. Split input into 2 regimes

  2. if x < -4.240666482247368e+50 or 1.2788878625888583e+86 < x

    1. Initial program 0.7

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

    2. Applied simplify32.9

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

    4. Applied associate-*l/17.8

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

    6. Applied pow-to-exp17.8

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

    7. Applied div-exp12.0

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

    8. Applied pow-to-exp12.5

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

    9. Applied div-exp0.7

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

    if -4.240666482247368e+50 < x < 1.2788878625888583e+86

    1. Initial program 2.7

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

    2. Applied simplify17.2

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

    4. Applied pow-to-exp17.2

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

    5. Applied div-exp11.6

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

    6. Applied pow-to-exp12.6

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

    7. Applied div-exp1.7

      \[\leadsto \frac{x}{y} \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - \left(b - \log z \cdot y\right)}}\]
  3. Recombined 2 regimes into one program.
  4. Removed slow pow expressions.

Runtime

Time bar (total: 3.7m)Debug logProfile

herbie shell --seed '#(1063282112 2455465480 4141627379 3773598652 1647277307 776739644)' 
(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))