Average Error: 2.1 → 1.0
Time: 3.3m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{e^{b} \cdot \frac{\frac{\frac{y}{x}}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \le 7.689487003288736 \cdot 10^{+145}:\\ \;\;\;\;\frac{1}{e^{b} \cdot \frac{\frac{\frac{y}{x}}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\\ \end{array}\]

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 (* (exp b) (/ (/ (/ y x) (pow z y)) (pow a (- t 1.0))))) < 7.689487003288736e+145

    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 sub-neg3.0

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

    4. Applied exp-sum3.0

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

    5. Applied simplify2.2

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

    7. Applied clear-num2.2

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

    8. Applied simplify1.3

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

    if 7.689487003288736e+145 < (/ 1 (* (exp b) (/ (/ (/ y x) (pow z y)) (pow a (- t 1.0)))))

    1. Initial program 0.5

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

Runtime

Time bar (total: 3.3m)Debug logProfile

herbie shell --seed '#(1072840222 1305617769 1692503039 1353360431 4178980589 1488672652)' +o rules:numerics
(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))