Average Error: 1.9 → 0.2
Time: 1.6m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left({a}^{\left(-1.0\right)} \cdot {z}^{y}\right) \cdot {a}^{t}}{\frac{y}{x} \cdot e^{b}} \le -6.767707010946977 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{t}}{{a}^{1.0}} \cdot e^{-b}}{y}\\ \mathbf{if}\;\frac{\left({a}^{\left(-1.0\right)} \cdot {z}^{y}\right) \cdot {a}^{t}}{\frac{y}{x} \cdot e^{b}} \le 8.742842592298168 \cdot 10^{+273}:\\ \;\;\;\;\frac{\left({a}^{\left(-1.0\right)} \cdot {z}^{y}\right) \cdot {a}^{t}}{\frac{y}{x} \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\\ \end{array}\]

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 3 regimes

  2. if (/ (* (* (pow a (- 1.0)) (pow z y)) (pow a t)) (* (/ y x) (exp b))) < -6.767707010946977e+29

    1. Initial program 6.1

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

    3. Applied sub-neg6.1

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

    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. Applied associate-*r*5.9

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

    6. Applied simplify0.9

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

    8. Applied pow-sub0.6

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

    9. Applied associate-*r/0.5

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

    if -6.767707010946977e+29 < (/ (* (* (pow a (- 1.0)) (pow z y)) (pow a t)) (* (/ y x) (exp b))) < 8.742842592298168e+273

    1. Initial program 2.5

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

    2. Taylor expanded around inf 2.5

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

    3. Applied simplify0.1

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

    if 8.742842592298168e+273 < (/ (* (* (pow a (- 1.0)) (pow z y)) (pow a t)) (* (/ y x) (exp b)))

    1. Initial program 0.3

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

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed 2018296 
(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))