Average Error: 2.0 → 0.7
Time: 2.2m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 7.814213043956812 \cdot 10^{-163} \lor \neg \left(\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 1.88510480953367 \cdot 10^{+301}\right):\\ \;\;\;\;\frac{x \cdot {\left(e^{\sqrt[3]{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot \sqrt[3]{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b}}\right)}^{\left(\sqrt[3]{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b}\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot e^{b}}{{z}^{y} \cdot {a}^{\left(t - 1.0\right)}}}\\ \end{array}\]

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 (/ (exp b) (pow a (- t 1.0))) < 7.814213043956812e-163 or 1.88510480953367e+301 < (/ (exp b) (pow a (- t 1.0)))

    1. Initial program 0.3

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

    3. Applied add-cube-cbrt0.4

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(\sqrt[3]{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b} \cdot \sqrt[3]{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right) \cdot \sqrt[3]{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}{y}\]

    4. Applied exp-prod0.4

      \[\leadsto \frac{x \cdot \color{blue}{{\left(e^{\sqrt[3]{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b} \cdot \sqrt[3]{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}^{\left(\sqrt[3]{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right)}}}{y}\]

    if 7.814213043956812e-163 < (/ (exp b) (pow a (- t 1.0))) < 1.88510480953367e+301

    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 associate-/l*4.4

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

    4. Applied simplify1.6

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

  4. Applied simplify0.7

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 7.814213043956812 \cdot 10^{-163} \lor \neg \left(\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 1.88510480953367 \cdot 10^{+301}\right):\\ \;\;\;\;\frac{x \cdot {\left(e^{\sqrt[3]{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot \sqrt[3]{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b}}\right)}^{\left(\sqrt[3]{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b}\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot e^{b}}{{z}^{y} \cdot {a}^{\left(t - 1.0\right)}}}\\ \end{array}}\]

Runtime

Time bar (total: 2.2m)Debug logProfile

herbie shell --seed 2020178 
(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))