Average Error: 1.9 → 1.0
Time: 2.6m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\frac{e^{b}}{\frac{{z}^{y}}{y}}} \le -2.030640281883843 \cdot 10^{+302} \lor \neg \left(\frac{x}{\frac{e^{b}}{\frac{{z}^{y}}{y}}} \le -2.2168054990413952 \cdot 10^{-259}\right):\\ \;\;\;\;\frac{x \cdot {e}^{\left(\left(\left(t - 1.0\right) \cdot \log a + y \cdot \log z\right) - b\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{\left(\frac{1}{z}\right)}^{\left(-y\right)}}{\frac{y}{x}}}{e^{b} \cdot {\left(\frac{1}{a}\right)}^{\left(t - 1.0\right)}}\\ \end{array}\]

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if (/ x (/ (exp b) (/ (pow z y) y))) < -2.030640281883843e+302 or -2.2168054990413952e-259 < (/ x (/ (exp b) (/ (pow z y) y)))

    1. Initial program 1.1

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

    3. Applied *-un-lft-identity1.1

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

    4. Applied exp-prod1.1

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

    5. Applied simplify1.1

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

    if -2.030640281883843e+302 < (/ x (/ (exp b) (/ (pow z y) y))) < -2.2168054990413952e-259

    1. Initial program 7.7

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

    3. Applied exp-diff7.7

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

    4. Applied simplify5.4

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

    5. Taylor expanded around inf 7.7

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

    6. Applied simplify0.4

      \[\leadsto \color{blue}{\frac{\frac{{\left(\frac{1}{z}\right)}^{\left(-y\right)}}{\frac{y}{x}}}{\frac{e^{b}}{1} \cdot {\left(\frac{1}{a}\right)}^{\left(t - 1.0\right)}}}\]
  3. Recombined 2 regimes into one program.

  4. Applied simplify1.0

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{x}{\frac{e^{b}}{\frac{{z}^{y}}{y}}} \le -2.030640281883843 \cdot 10^{+302} \lor \neg \left(\frac{x}{\frac{e^{b}}{\frac{{z}^{y}}{y}}} \le -2.2168054990413952 \cdot 10^{-259}\right):\\ \;\;\;\;\frac{x \cdot {e}^{\left(\left(\left(t - 1.0\right) \cdot \log a + y \cdot \log z\right) - b\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{\left(\frac{1}{z}\right)}^{\left(-y\right)}}{\frac{y}{x}}}{e^{b} \cdot {\left(\frac{1}{a}\right)}^{\left(t - 1.0\right)}}\\ \end{array}}\]

Runtime

Time bar (total: 2.6m)Debug logProfile

herbie shell --seed 2019053 +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))