Average Error: 1.8 → 0.7
Time: 2.1m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{{z}^{y} \cdot {a}^{\left(-1.0\right)}}{\left(\left(\sqrt[3]{\frac{y}{x} \cdot e^{b}} \cdot \sqrt[3]{\frac{y}{x} \cdot e^{b}}\right) \cdot \sqrt[3]{\frac{y}{x} \cdot e^{b}}\right) \cdot {a}^{\left(-t\right)}} \le 5.174179268694064 \cdot 10^{+240}:\\ \;\;\;\;\frac{{z}^{y} \cdot {a}^{\left(-1.0\right)}}{\left(\frac{y}{x} \cdot e^{b}\right) \cdot {a}^{\left(-t\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\\ \end{array}\]

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) (pow a (- 1.0))) (* (* (* (cbrt (* (/ y x) (exp b))) (cbrt (* (/ y x) (exp b)))) (cbrt (* (/ y x) (exp b)))) (pow a (- t)))) < 5.174179268694064e+240

    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. Taylor expanded around inf 2.7

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

    3. Applied simplify0.9

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

    if 5.174179268694064e+240 < (/ (* (pow z y) (pow a (- 1.0))) (* (* (* (cbrt (* (/ y x) (exp b))) (cbrt (* (/ y x) (exp b)))) (cbrt (* (/ y x) (exp b)))) (pow a (- t))))

    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 2018206 
(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))