Average Error: 2.0 → 1.3
Time: 2.2m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y} \le -1.0129306349004452 \cdot 10^{-306} \lor \neg \left(\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y} \le 1.4738404403187998 \cdot 10^{-272}\right):\\ \;\;\;\;\frac{x \cdot \left(e^{-b} \cdot \left({a}^{\left(t - 1.0\right)} \cdot {z}^{y}\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b} \cdot \left(e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b} \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right)} \cdot x}{y}\\ \end{array}\]

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) < -1.0129306349004452e-306 or 1.4738404403187998e-272 < (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

    1. Initial program 6.0

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

    3. Applied sub-neg6.0

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

    4. Applied exp-sum6.0

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

    5. Simplified1.2

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

    if -1.0129306349004452e-306 < (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y) < 1.4738404403187998e-272

    1. Initial program 1.3

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

    3. Applied add-cbrt-cube1.3

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y} \le -1.0129306349004452 \cdot 10^{-306} \lor \neg \left(\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y} \le 1.4738404403187998 \cdot 10^{-272}\right):\\ \;\;\;\;\frac{x \cdot \left(e^{-b} \cdot \left({a}^{\left(t - 1.0\right)} \cdot {z}^{y}\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b} \cdot \left(e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b} \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right)} \cdot x}{y}\\ \end{array}\]

Runtime

Time bar (total: 2.2m)Debug logProfile

herbie shell --seed 2018216 
(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))