Average Error: 1.9 → 0.7
Time: 2.0m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 1.1387342801657947 \cdot 10^{-151} \lor \neg \left(\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 3.8162688269731978 \cdot 10^{+295}\right):\\ \;\;\;\;\frac{e^{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left({z}^{y} \cdot {a}^{t}\right) \cdot x}{y \cdot \left(e^{b} \cdot {a}^{1.0}\right)}\\ \end{array}\]

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))) < 1.1387342801657947e-151 or 3.8162688269731978e+295 < (/ (exp b) (pow a (- t 1.0)))

    1. Initial program 0.3

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

    if 1.1387342801657947e-151 < (/ (exp b) (pow a (- t 1.0))) < 3.8162688269731978e+295

    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 sub-neg7.3

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

    4. Applied exp-sum7.3

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

    5. Applied simplify4.9

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

    7. Applied exp-neg5.0

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

    8. Applied pow-sub4.8

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

    9. Applied associate-*l/4.8

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

    10. Applied frac-times4.8

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

    11. Applied associate-*r/4.8

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

    12. Applied associate-/l/1.8

      \[\leadsto \color{blue}{\frac{x \cdot \left(\left({a}^{t} \cdot {z}^{y}\right) \cdot 1\right)}{y \cdot \left({a}^{1.0} \cdot e^{b}\right)}}\]
  3. Recombined 2 regimes into one program.

  4. Applied simplify0.7

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 1.1387342801657947 \cdot 10^{-151} \lor \neg \left(\frac{e^{b}}{{a}^{\left(t - 1.0\right)}} \le 3.8162688269731978 \cdot 10^{+295}\right):\\ \;\;\;\;\frac{e^{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left({z}^{y} \cdot {a}^{t}\right) \cdot x}{y \cdot \left(e^{b} \cdot {a}^{1.0}\right)}\\ \end{array}}\]

Runtime

Time bar (total: 2.0m)Debug logProfile

herbie shell --seed 2018207 
(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))