Average Error: 29.4 → 25.3
Time: 12.2s
Precision: 64
Internal Precision: 2368
$\left(-p\right) + \sqrt{{p}^{2} + q}$
$\begin{array}{l} \mathbf{if}\;p \le 9.80074659114093 \cdot 10^{+117}:\\ \;\;\;\;\sqrt{p \cdot p + q} - p\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Split input into 2 regimes
2. ## if p < 9.80074659114093e+117

1. Initial program 21.5

$\left(-p\right) + \sqrt{{p}^{2} + q}$
2. Initial simplification21.5

$\leadsto \sqrt{q + p \cdot p} - p$

## if 9.80074659114093e+117 < p

1. Initial program 59.8

$\left(-p\right) + \sqrt{{p}^{2} + q}$
2. Initial simplification59.8

$\leadsto \sqrt{q + p \cdot p} - p$
3. Taylor expanded around 0 40.1

$\leadsto \color{blue}{0}$
3. Recombined 2 regimes into one program.
4. Final simplification25.3

$\leadsto \begin{array}{l} \mathbf{if}\;p \le 9.80074659114093 \cdot 10^{+117}:\\ \;\;\;\;\sqrt{p \cdot p + q} - p\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}$

# Runtime

Time bar (total: 12.2s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (p q)
:name "-p + sqrt(p^2 + q)"
(+ (- p) (sqrt (+ (pow p 2) q))))