Average Error: 35.8 → 24.5
Time: 7.4s
Precision: 64
Internal Precision: 320
$\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}$
$\begin{array}{l} \mathbf{if}\;x \le -5.77126452019715 \cdot 10^{+140}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le 1.6019685912508635 \cdot 10^{+155}:\\ \;\;\;\;\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}$

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Results

 In Out
Enter valid numbers for all inputs

Derivation

1. Split input into 3 regimes
2. if x < -5.77126452019715e+140

1. Initial program 56.3

$\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}$
2. Taylor expanded around -inf 15.6

$\leadsto \color{blue}{-1 \cdot x}$
3. Simplified15.6

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

if -5.77126452019715e+140 < x < 1.6019685912508635e+155

1. Initial program 28.0

$\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}$

if 1.6019685912508635e+155 < x

1. Initial program 59.2

$\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}$
2. Taylor expanded around inf 13.4

$\leadsto \color{blue}{x}$
3. Recombined 3 regimes into one program.
4. Final simplification24.5

$\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.77126452019715 \cdot 10^{+140}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le 1.6019685912508635 \cdot 10^{+155}:\\ \;\;\;\;\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}$

Runtime

Time bar (total: 7.4s)Debug log

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