Average Error: 7.5 → 4.3
Time: 19.6s
Precision: 64
Internal Precision: 320
$\sqrt{x + a \cdot x}$
$\begin{array}{l} \mathbf{if}\;x + x \cdot a \le 8.311562281807733 \cdot 10^{+285}:\\ \;\;\;\;\sqrt{x + x \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{1 + a} \cdot \sqrt{x}\\ \end{array}$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Split input into 2 regimes
2. ## if (+ x (* a x)) < 8.311562281807733e+285

1. Initial program 0.1

$\sqrt{x + a \cdot x}$

## if 8.311562281807733e+285 < (+ x (* a x))

1. Initial program 46.9

$\sqrt{x + a \cdot x}$
2. Using strategy rm
3. Applied distribute-rgt1-in46.9

$\leadsto \sqrt{\color{blue}{\left(a + 1\right) \cdot x}}$
4. Applied sqrt-prod26.7

$\leadsto \color{blue}{\sqrt{a + 1} \cdot \sqrt{x}}$
3. Recombined 2 regimes into one program.
4. Final simplification4.3

$\leadsto \begin{array}{l} \mathbf{if}\;x + x \cdot a \le 8.311562281807733 \cdot 10^{+285}:\\ \;\;\;\;\sqrt{x + x \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{1 + a} \cdot \sqrt{x}\\ \end{array}$

# Runtime

Time bar (total: 19.6s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x a)
:name "sqrt(x + a*x)"
(sqrt (+ x (* a x))))