Average Error: 1.8 → 1.1
Time: 1.9m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 2.9424119376297374 \cdot 10^{-286} \lor \neg \left(\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 1.6367329525816681 \cdot 10^{+301}\right):\\ \;\;\;\;\frac{{e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{t} \cdot \left({z}^{y} \cdot {a}^{\left(-1.0\right)}\right)}{\frac{y}{x} \cdot e^{b}}\\ \end{array}\]

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 (/ (exp b) (pow a (- t 1.0))) < 2.9424119376297374e-286 or 1.6367329525816681e+301 < (/ (exp b) (pow a (- t 1.0)))

    1. Initial program 0.1

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

    3. Applied *-un-lft-identity0.1

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

    4. Applied exp-prod0.1

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

    5. Applied simplify0.1

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

    if 2.9424119376297374e-286 < (/ (exp b) (pow a (- t 1.0))) < 1.6367329525816681e+301

    1. Initial program 6.1

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

    2. Taylor expanded around inf 6.0

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

    3. Applied simplify3.7

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

  4. Applied simplify1.1

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 2.9424119376297374 \cdot 10^{-286} \lor \neg \left(\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 1.6367329525816681 \cdot 10^{+301}\right):\\ \;\;\;\;\frac{{e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{t} \cdot \left({z}^{y} \cdot {a}^{\left(-1.0\right)}\right)}{\frac{y}{x} \cdot e^{b}}\\ \end{array}}\]

Runtime

Time bar (total: 1.9m)Debug logProfile

herbie shell --seed '#(1071852389 864846987 1238109217 3425890003 4124793586 650694553)' 
(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))