Average Error: 2.0 → 1.3
Time: 4.2m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 1.8137471594957846 \cdot 10^{-278} \lor \neg \left(\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 1.0459909917573926 \cdot 10^{+295}\right):\\ \;\;\;\;\frac{{\left(e^{\sqrt[3]{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot \sqrt[3]{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b}}\right)}^{\left(\sqrt[3]{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b}\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot \frac{{z}^{y}}{\frac{y}{x}}\\ \end{array}\]

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 (/ (pow a (- t 1.0)) (exp b)) < 1.8137471594957846e-278 or 1.0459909917573926e+295 < (/ (pow a (- t 1.0)) (exp b))

    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 1.8137471594957846e-278 < (/ (pow a (- t 1.0)) (exp b)) < 1.0459909917573926e+295

    1. Initial program 6.6

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

    2. Applied simplify4.1

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

  4. Applied simplify1.3

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 1.8137471594957846 \cdot 10^{-278} \lor \neg \left(\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 1.0459909917573926 \cdot 10^{+295}\right):\\ \;\;\;\;\frac{{\left(e^{\sqrt[3]{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot \sqrt[3]{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b}}\right)}^{\left(\sqrt[3]{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b}\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot \frac{{z}^{y}}{\frac{y}{x}}\\ \end{array}}\]

Runtime

Time bar (total: 4.2m)Debug logProfile

herbie shell --seed 2018166 
(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))