Average Error: 1.9 → 0.6
Time: 2.3m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{x}{\frac{e^{b} \cdot y}{{z}^{y} \cdot {a}^{t}}}}{{a}^{1.0}} \le 1.2606901629962577 \cdot 10^{+297}:\\ \;\;\;\;\frac{\frac{x}{\frac{e^{b} \cdot y}{{z}^{y} \cdot {a}^{t}}}}{{a}^{1.0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\\ \end{array}\]

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 (/ (/ x (/ (* (exp b) y) (* (pow z y) (pow a t)))) (pow a 1.0)) < 1.2606901629962577e+297

    1. Initial program 2.5

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

    3. Applied associate-/l*2.5

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

    4. Applied simplify1.7

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

    6. Applied pow-sub1.6

      \[\leadsto \frac{x}{\frac{e^{b} \cdot y}{{z}^{y} \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1.0}}}}}\]

    7. Applied associate-*r/1.6

      \[\leadsto \frac{x}{\frac{e^{b} \cdot y}{\color{blue}{\frac{{z}^{y} \cdot {a}^{t}}{{a}^{1.0}}}}}\]

    8. Applied associate-/r/1.6

      \[\leadsto \frac{x}{\color{blue}{\frac{e^{b} \cdot y}{{z}^{y} \cdot {a}^{t}} \cdot {a}^{1.0}}}\]

    9. Applied associate-/r*0.8

      \[\leadsto \color{blue}{\frac{\frac{x}{\frac{e^{b} \cdot y}{{z}^{y} \cdot {a}^{t}}}}{{a}^{1.0}}}\]

    if 1.2606901629962577e+297 < (/ (/ x (/ (* (exp b) y) (* (pow z y) (pow a t)))) (pow a 1.0))

    1. Initial program 0.3

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

Runtime

Time bar (total: 2.3m)Debug logProfile

herbie shell --seed 2018195 
(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))