Average Error: 2.0 → 1.5
Time: 1.7m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y} \le -7.999887503508039 \cdot 10^{-179} \lor \neg \left(\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y} \le 0.0\right):\\ \;\;\;\;\frac{\left(\left({a}^{\left(-1.0\right)} \cdot {z}^{y}\right) \cdot \left(e^{-b} \cdot {a}^{t}\right)\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y} \cdot \left(\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y} \cdot \frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}\right)}\\ \end{array}\]

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 (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y) < -7.999887503508039e-179 or 0.0 < (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

    1. Initial program 5.9

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

    2. Taylor expanded around inf 5.9

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

    3. Simplified0.9

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

    if -7.999887503508039e-179 < (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y) < 0.0

    1. Initial program 1.4

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

    3. Applied add-cbrt-cube1.6

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y} \le -7.999887503508039 \cdot 10^{-179} \lor \neg \left(\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y} \le 0.0\right):\\ \;\;\;\;\frac{\left(\left({a}^{\left(-1.0\right)} \cdot {z}^{y}\right) \cdot \left(e^{-b} \cdot {a}^{t}\right)\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y} \cdot \left(\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y} \cdot \frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}\right)}\\ \end{array}\]

Runtime

Time bar (total: 1.7m)Debug logProfile

herbie shell --seed 2018219 
(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))