Average Error: 6.2 → 0.1
Time: 56.3s
Precision: 64
Internal Precision: 320
$e^{\left(\left(\left(log \cdot a + log \cdot b\right) + log \cdot c\right) + log \cdot d\right) + log \cdot e}$
$\begin{array}{l} \mathbf{if}\;e^{\left(\left(\left(log \cdot a + log \cdot b\right) + log \cdot c\right) + log \cdot d\right) + log \cdot e} \le 5.747936617440744 \cdot 10^{+19}:\\ \;\;\;\;e^{\left(\left(\left(log \cdot a + log \cdot b\right) + log \cdot c\right) + log \cdot d\right) + log \cdot e}\\ \mathbf{else}:\\ \;\;\;\;{\left(e^{log}\right)}^{\left(e + \left(\left(c + d\right) + \left(a + b\right)\right)\right)}\\ \end{array}$

# Try it out

Your Program's Arguments

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Split input into 2 regimes
2. ## if (exp (+ (+ (+ (+ (* log a) (* log b)) (* log c)) (* log d)) (* log e))) < 5.747936617440744e+19

1. Initial program 0.0

$e^{\left(\left(\left(log \cdot a + log \cdot b\right) + log \cdot c\right) + log \cdot d\right) + log \cdot e}$

## if 5.747936617440744e+19 < (exp (+ (+ (+ (+ (* log a) (* log b)) (* log c)) (* log d)) (* log e)))

1. Initial program 62.3

$e^{\left(\left(\left(log \cdot a + log \cdot b\right) + log \cdot c\right) + log \cdot d\right) + log \cdot e}$
2. Applied simplify0.8

$\leadsto \color{blue}{{\left(e^{log}\right)}^{\left(e + \left(\left(c + d\right) + \left(a + b\right)\right)\right)}}$
3. Recombined 2 regimes into one program.

# Runtime

Time bar (total: 56.3s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (log a b c d e)
:name "exp(log a + log b + log c + log d + log e)"
(exp (+ (+ (+ (+ (* log a) (* log b)) (* log c)) (* log d)) (* log e))))