Average Error: 1.8 → 0.6
Time: 4.7m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\sqrt[3]{\frac{\frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}{\frac{\frac{y}{x}}{{z}^{y}}}} \cdot \sqrt[3]{\frac{\frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}{\frac{\frac{y}{x}}{{z}^{y}}}}\right) \cdot \sqrt[3]{\frac{{z}^{y}}{y} \cdot \left({a}^{\left(t - 1.0\right)} \cdot \frac{x}{e^{b}}\right)} \le 6.152959373194397 \cdot 10^{+257}:\\ \;\;\;\;\frac{\left({z}^{y} \cdot {a}^{\left(-1.0\right)}\right) \cdot {a}^{t}}{\frac{y}{x} \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}\right) \cdot \frac{1}{y}\\ \end{array}\]

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if (* (* (cbrt (/ (/ (pow a (- t 1.0)) (exp b)) (/ (/ y x) (pow z y)))) (cbrt (/ (/ (pow a (- t 1.0)) (exp b)) (/ (/ y x) (pow z y))))) (cbrt (* (/ (pow z y) y) (* (pow a (- t 1.0)) (/ x (exp b)))))) < 6.152959373194397e+257

    1. Initial program 2.7

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

    2. Taylor expanded around inf 2.7

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

    3. Applied simplify0.8

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

    if 6.152959373194397e+257 < (* (* (cbrt (/ (/ (pow a (- t 1.0)) (exp b)) (/ (/ y x) (pow z y)))) (cbrt (/ (/ (pow a (- t 1.0)) (exp b)) (/ (/ y x) (pow z y))))) (cbrt (* (/ (pow z y) y) (* (pow a (- t 1.0)) (/ x (exp b))))))

    1. Initial program 0.3

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

    3. Applied div-inv0.3

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

Runtime

Time bar (total: 4.7m)Debug logProfile

herbie shell --seed 2018193 
(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))