Average Error: 1.9 → 0.7
Time: 2.1m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{{a}^{t} \cdot {z}^{y}}{{a}^{1.0}}}{y \cdot \frac{e^{b}}{x}} \le 1.2606901629962579 \cdot 10^{+297}:\\ \;\;\;\;\frac{\frac{{a}^{t} \cdot {z}^{y}}{{a}^{1.0}}}{y \cdot \frac{e^{b}}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\\ \end{array}\]

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 2 regimes

  2. if (/ (/ (* (pow a t) (pow z y)) (pow a 1.0)) (* y (/ (exp b) x))) < 1.2606901629962579e+297

    1. Initial program 2.6

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

    2. Taylor expanded around inf 2.6

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

    3. Applied simplify0.9

      \[\leadsto \color{blue}{\frac{\frac{{a}^{t} \cdot {z}^{y}}{{a}^{1.0}}}{y \cdot \frac{e^{b}}{x}}}\]

    if 1.2606901629962579e+297 < (/ (/ (* (pow a t) (pow z y)) (pow a 1.0)) (* y (/ (exp b) x)))

    1. Initial program 0.2

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

Runtime

Time bar (total: 2.1m)Debug logProfile

herbie shell --seed 2018195 +o rules:numerics
(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))