Average Error: 30.1 → 17.0
Time: 4.1s
Precision: 64
Internal Precision: 320
$\sqrt{a \cdot a + b \cdot b}$
$\begin{array}{l} \mathbf{if}\;a \le -5.147403001023096 \cdot 10^{+84}:\\ \;\;\;\;-a\\ \mathbf{elif}\;a \le 1.7967825844854412 \cdot 10^{+130}:\\ \;\;\;\;\sqrt{a \cdot a + b \cdot b}\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array}$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Split input into 3 regimes
2. ## if a < -5.147403001023096e+84

1. Initial program 45.3

$\sqrt{a \cdot a + b \cdot b}$
2. Taylor expanded around -inf 10.5

$\leadsto \color{blue}{-1 \cdot a}$
3. Simplified10.5

$\leadsto \color{blue}{-a}$

## if -5.147403001023096e+84 < a < 1.7967825844854412e+130

1. Initial program 20.5

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

## if 1.7967825844854412e+130 < a

1. Initial program 53.8

$\sqrt{a \cdot a + b \cdot b}$
2. Taylor expanded around inf 9.7

$\leadsto \color{blue}{a}$
3. Recombined 3 regimes into one program.
4. Final simplification17.0

$\leadsto \begin{array}{l} \mathbf{if}\;a \le -5.147403001023096 \cdot 10^{+84}:\\ \;\;\;\;-a\\ \mathbf{elif}\;a \le 1.7967825844854412 \cdot 10^{+130}:\\ \;\;\;\;\sqrt{a \cdot a + b \cdot b}\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array}$

# Runtime

Time bar (total: 4.1s)Debug log

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