Average Error: 1.9 → 1.4
Time: 2.3m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 3.2378447176585645 \cdot 10^{-212} \lor \neg \left(\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 1.5128378188808067 \cdot 10^{+264}\right):\\ \;\;\;\;\frac{e^{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{t} \cdot \left({z}^{y} \cdot {a}^{\left(-1.0\right)}\right)}{e^{b} \cdot \frac{y}{x}}\\ \end{array}\]

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

Derivation

  1. Split input into 2 regimes

  2. if (/ (pow a (- t 1.0)) (exp b)) < 3.2378447176585645e-212 or 1.5128378188808067e+264 < (/ (pow a (- t 1.0)) (exp b))

    1. Initial program 0.9

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

    if 3.2378447176585645e-212 < (/ (pow a (- t 1.0)) (exp b)) < 1.5128378188808067e+264

    1. Initial program 5.6

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

    2. Taylor expanded around inf 5.6

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

    3. Applied simplify3.3

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

  4. Applied simplify1.4

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 3.2378447176585645 \cdot 10^{-212} \lor \neg \left(\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 1.5128378188808067 \cdot 10^{+264}\right):\\ \;\;\;\;\frac{e^{\left(y \cdot \log z + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{t} \cdot \left({z}^{y} \cdot {a}^{\left(-1.0\right)}\right)}{e^{b} \cdot \frac{y}{x}}\\ \end{array}}\]

Runtime

Time bar (total: 2.3m)Debug logProfile

herbie shell --seed '#(1072107073 2127697367 3936270018 2300570620 2134894798 4023771849)' 
(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))