Average Error: 2.0 → 1.2
Time: 3.8m
Precision: 64
Internal Precision: 384
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{e^{b} \cdot \frac{\frac{\frac{y}{x}}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \le +\infty:\\ \;\;\;\;\frac{\frac{{a}^{t} \cdot x}{\frac{e^{b}}{-{z}^{y}} \cdot {a}^{1.0}}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\\ \end{array}\]

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

Derivation

  1. Split input into 2 regimes

  2. if (/ 1 (* (exp b) (/ (/ (/ y x) (pow z y)) (pow a (- t 1.0))))) < +inf.0

    1. Initial program 3.0

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

    3. Applied frac-2neg3.0

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

    4. Applied simplify3.9

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

    6. Applied pow-sub3.8

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

    7. Applied associate-*l/3.8

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

    8. Applied associate-/l/1.9

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

    if +inf.0 < (/ 1 (* (exp b) (/ (/ (/ y x) (pow z y)) (pow a (- t 1.0)))))

    1. Initial program 0.0

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

Runtime

Time bar (total: 3.8m)Debug logProfile

herbie shell --seed '#(1070706311 3771791028 4128836681 4194990999 2341756049 504035650)' 
(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))