Average Error: 1.8 → 1.0
Time: 1.6m
Precision: 64
Internal Precision: 384
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{\frac{\frac{y}{x} \cdot \frac{e^{b}}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \le 4.8049601633006355 \cdot 10^{+244}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{z}^{y}}{e^{b}} \cdot {a}^{\left(t - 1.0\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\\ \end{array}\]

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 (/ (* (/ y x) (/ (exp b) (pow z y))) (pow a (- t 1.0)))) < 4.8049601633006355e+244

    1. Initial program 2.6

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

    3. Applied associate-/l*2.3

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

    4. Applied simplify1.4

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

    if 4.8049601633006355e+244 < (/ 1 (/ (* (/ y x) (/ (exp b) (pow z y))) (pow a (- t 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: 1.6m)Debug logProfile

herbie shell --seed '#(1070355188 2193211668 3977393919 3454156579 3755371326 1656365382)' 
(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))