Average Error: 2.0 → 0.7
Time: 2.4m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 1.2061963707571028 \cdot 10^{-294} \lor \neg \left(\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 2.473923949799292 \cdot 10^{+152}\right):\\ \;\;\;\;\frac{{e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot {z}^{y}}}\\ \end{array}\]

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 (/ (pow a (- t 1.0)) (exp b)) < 1.2061963707571028e-294 or 2.473923949799292e+152 < (/ (pow a (- t 1.0)) (exp b))

    1. Initial program 0.4

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

    3. Applied *-un-lft-identity0.4

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

    4. Applied exp-prod0.4

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

    5. Applied simplify0.4

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

    if 1.2061963707571028e-294 < (/ (pow a (- t 1.0)) (exp b)) < 2.473923949799292e+152

    1. Initial program 7.7

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

    3. Applied associate--l+7.7

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

    4. Applied exp-sum7.7

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

    5. Applied simplify7.7

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

    6. Applied simplify5.3

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

    8. Applied associate-/l*1.9

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

  4. Applied simplify0.7

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 1.2061963707571028 \cdot 10^{-294} \lor \neg \left(\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \le 2.473923949799292 \cdot 10^{+152}\right):\\ \;\;\;\;\frac{{e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot {z}^{y}}}\\ \end{array}}\]

Runtime

Time bar (total: 2.4m)Debug logProfile

herbie shell --seed '#(1071948828 1180510430 2986424009 997076509 406109801 420189285)' 
(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))