Average Error: 30.1 → 17.0
Time: 4.6s
Precision: 64
Internal Precision: 320
$\sqrt{{x}^{2} + {y}^{2}}$
$\begin{array}{l} \mathbf{if}\;x \le -5.147403001023096 \cdot 10^{+84}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le 1.7967825844854412 \cdot 10^{+130}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

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

1. Initial program 45.3

$\sqrt{{x}^{2} + {y}^{2}}$
2. Initial simplification45.3

$\leadsto \sqrt{x \cdot x + y \cdot y}$
3. Taylor expanded around -inf 10.5

$\leadsto \color{blue}{-1 \cdot x}$
4. Simplified10.5

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

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

1. Initial program 20.5

$\sqrt{{x}^{2} + {y}^{2}}$
2. Initial simplification20.5

$\leadsto \sqrt{x \cdot x + y \cdot y}$

## if 1.7967825844854412e+130 < x

1. Initial program 53.8

$\sqrt{{x}^{2} + {y}^{2}}$
2. Initial simplification53.8

$\leadsto \sqrt{x \cdot x + y \cdot y}$
3. Taylor expanded around inf 9.7

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

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

# Runtime

Time bar (total: 4.6s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x y)
:name "sqrt(pow(x,2)+pow(y,2))"
(sqrt (+ (pow x 2) (pow y 2))))