Average Error: 1.9 → 2.8
Time: 3.2m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 1.7356790566953636 \cdot 10^{-250} \lor \neg \left(x \le 6.706783453291331 \cdot 10^{-145}\right):\\ \;\;\;\;\frac{x}{\frac{y}{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left({a}^{\left(-1.0\right)} \cdot {z}^{y}\right) \cdot {a}^{t}}{\frac{y}{x} \cdot e^{b}}\\ \end{array}\]

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 x < 1.7356790566953636e-250 or 6.706783453291331e-145 < x

    1. Initial program 1.7

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

    3. Applied associate-/l*1.6

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

    if 1.7356790566953636e-250 < x < 6.706783453291331e-145

    1. Initial program 4.1

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

    2. Taylor expanded around inf 4.1

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

    3. Simplified14.5

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

  4. Final simplification2.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 1.7356790566953636 \cdot 10^{-250} \lor \neg \left(x \le 6.706783453291331 \cdot 10^{-145}\right):\\ \;\;\;\;\frac{x}{\frac{y}{e^{\left(\log a \cdot \left(t - 1.0\right) + y \cdot \log z\right) - b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left({a}^{\left(-1.0\right)} \cdot {z}^{y}\right) \cdot {a}^{t}}{\frac{y}{x} \cdot e^{b}}\\ \end{array}\]

Runtime

Time bar (total: 3.2m)Debug logProfile

herbie shell --seed 2018225 
(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))