Average Error: 1.9 → 0.1
Time: 2.8m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{e^{b} \cdot y}{{z}^{y} \cdot {a}^{\left(t - 1.0\right)}} \le -2.891078416329484 \cdot 10^{-182}:\\ \;\;\;\;\frac{x}{\frac{e^{b} \cdot y}{{z}^{y} \cdot {a}^{\left(t - 1.0\right)}}}\\ \mathbf{if}\;\frac{e^{b} \cdot y}{{z}^{y} \cdot {a}^{\left(t - 1.0\right)}} \le 1.0374368783999238 \cdot 10^{-204}:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {z}^{y}}{\frac{e^{b}}{{a}^{\left(t - 1.0\right)}}}\\ \mathbf{if}\;\frac{e^{b} \cdot y}{{z}^{y} \cdot {a}^{\left(t - 1.0\right)}} \le 5.1898807126082994 \cdot 10^{+221}:\\ \;\;\;\;\frac{x}{\frac{e^{b} \cdot y}{{z}^{y} \cdot {a}^{\left(t - 1.0\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y}\\ \end{array}\]

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 3 regimes

  2. if (/ (* (exp b) y) (* (pow z y) (pow a (- t 1.0)))) < -2.891078416329484e-182 or 1.0374368783999238e-204 < (/ (* (exp b) y) (* (pow z y) (pow a (- t 1.0)))) < 5.1898807126082994e+221

    1. Initial program 3.8

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

    3. Applied associate-/l*1.5

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

    4. Applied simplify0.2

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

    if -2.891078416329484e-182 < (/ (* (exp b) y) (* (pow z y) (pow a (- t 1.0)))) < 1.0374368783999238e-204

    1. Initial program 6.1

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

    2. Taylor expanded around inf 6.1

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

    3. Applied simplify1.2

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

    if 5.1898807126082994e+221 < (/ (* (exp b) y) (* (pow z y) (pow a (- t 1.0))))

    1. Initial program 0.0

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

    3. Applied *-un-lft-identity0.0

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

    4. Applied exp-prod0.0

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

    5. Applied simplify0.0

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

Runtime

Time bar (total: 2.8m)Debug logProfile

herbie shell --seed 2018199 
(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))