Average Error: 1.8 → 0.8
Time: 3.2m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{{z}^{y}}{\frac{y}{x}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 2.079865453438447 \cdot 10^{+280}:\\ \;\;\;\;\frac{{z}^{y}}{\frac{y}{x}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\\ \end{array}\]

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 2 regimes

  2. if (* (/ (pow z y) (/ y x)) (/ (pow a (- t 1.0)) (exp b))) < 2.079865453438447e+280

    1. Initial program 2.7

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

    2. Applied simplify1.1

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

    if 2.079865453438447e+280 < (* (/ (pow z y) (/ y x)) (/ (pow a (- t 1.0)) (exp b)))

    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: 3.2m)Debug logProfile

herbie shell --seed 2018167 
(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))