Average Error: 1.8 → 1.0
Time: 2.6m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 6.0860463915201 \cdot 10^{-311} \lor \neg \left(\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 3.672579650136436 \cdot 10^{+181}\right):\\ \;\;\;\;\frac{\sqrt[3]{\left(e^{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x\right) \cdot \left(\left(e^{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x\right) \cdot \left(e^{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x\right)\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{e^{b}}}{{a}^{\left(-t\right)}}}{\frac{y}{{a}^{\left(-1.0\right)} \cdot {z}^{y}}}\\ \end{array}\]

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 1.0)) (exp b)) < 6.0860463915201e-311 or 3.672579650136436e+181 < (/ (pow a (- t 1.0)) (exp b))

    1. Initial program 0.2

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

    3. Applied add-cbrt-cube0.6

      \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\left(x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right) \cdot \left(x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right)\right) \cdot \left(x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right)}}}{y}\]

    if 6.0860463915201e-311 < (/ (pow a (- t 1.0)) (exp b)) < 3.672579650136436e+181

    1. Initial program 6.8

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

    2. Taylor expanded around inf 6.8

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

    3. Simplified4.3

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

    5. Applied associate-/l*2.3

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 6.0860463915201 \cdot 10^{-311} \lor \neg \left(\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 3.672579650136436 \cdot 10^{+181}\right):\\ \;\;\;\;\frac{\sqrt[3]{\left(e^{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x\right) \cdot \left(\left(e^{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x\right) \cdot \left(e^{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x\right)\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{e^{b}}}{{a}^{\left(-t\right)}}}{\frac{y}{{a}^{\left(-1.0\right)} \cdot {z}^{y}}}\\ \end{array}\]

Runtime

Time bar (total: 2.6m)Debug logProfile

herbie shell --seed 2018215 
(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))