Average Error: 2.0 → 0.8
Time: 2.2m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 3.501376709226839 \cdot 10^{-214} \lor \neg \left(\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 1.88510480953367 \cdot 10^{+301}\right):\\ \;\;\;\;\frac{x \cdot {\left(e^{\sqrt[3]{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot \sqrt[3]{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b}}\right)}^{\left(\sqrt[3]{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b}\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot e^{b}}{{a}^{t} \cdot \left({z}^{y} \cdot {a}^{\left(-1.0\right)}\right)}}\\ \end{array}\]

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))) < 3.501376709226839e-214 or 1.88510480953367e+301 < (/ (exp b) (pow a (- t 1.0)))

    1. Initial program 0.2

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

    3. Applied add-cube-cbrt0.3

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

    4. Applied exp-prod0.3

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

    if 3.501376709226839e-214 < (/ (exp b) (pow a (- t 1.0))) < 1.88510480953367e+301

    1. Initial program 7.3

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

    3. Applied associate-/l*5.1

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

    4. Applied simplify2.5

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

    6. Applied sub-neg2.5

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

    7. Applied unpow-prod-up2.4

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

    8. Applied associate-*l*2.4

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

  4. Applied simplify0.8

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 3.501376709226839 \cdot 10^{-214} \lor \neg \left(\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 1.88510480953367 \cdot 10^{+301}\right):\\ \;\;\;\;\frac{x \cdot {\left(e^{\sqrt[3]{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot \sqrt[3]{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b}}\right)}^{\left(\sqrt[3]{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b}\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot e^{b}}{{a}^{t} \cdot \left({z}^{y} \cdot {a}^{\left(-1.0\right)}\right)}}\\ \end{array}}\]

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))