Average Error: 2.1 → 1.0
Time: 2.9m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{x}{y} \cdot {z}^{y}}{\frac{e^{b}}{{a}^{\left(t - 1.0\right)}}} \le 7.689487003288736 \cdot 10^{+145}:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {z}^{y}}{\frac{e^{b}}{{a}^{\left(t - 1.0\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right) \cdot \frac{1}{y}\\ \end{array}\]

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 (/ (* (/ x y) (pow z y)) (/ (exp b) (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. Taylor expanded around inf 3.0

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

    3. Applied simplify1.2

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

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

    1. Initial program 0.5

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

    3. Applied div-inv0.5

      \[\leadsto \color{blue}{\left(x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right) \cdot \frac{1}{y}}\]
  3. Recombined 2 regimes into one program.

Runtime

Time bar (total: 2.9m)Debug logProfile

herbie shell --seed '#(1072840222 1305617769 1692503039 1353360431 4178980589 1488672652)' 
(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))