Average Error: 0.0 → 0.0
Time: 29.6s
Precision: 64
Internal Precision: 320
$\sqrt{\left(1 - x\right) \cdot \left(1 + x\right)}$
$\sqrt{\frac{\left(1 - x \cdot x\right) \cdot \left(x + 1\right)}{x + 1}}$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.0

$\sqrt{\left(1 - x\right) \cdot \left(1 + x\right)}$
2. Using strategy rm
3. Applied flip--0.0

$\leadsto \sqrt{\color{blue}{\frac{1 \cdot 1 - x \cdot x}{1 + x}} \cdot \left(1 + x\right)}$
4. Applied associate-*l/0.0

$\leadsto \sqrt{\color{blue}{\frac{\left(1 \cdot 1 - x \cdot x\right) \cdot \left(1 + x\right)}{1 + x}}}$
5. Simplified0.0

$\leadsto \sqrt{\frac{\color{blue}{\left(1 - x \cdot x\right) \cdot \left(1 + x\right)}}{1 + x}}$
6. Final simplification0.0

$\leadsto \sqrt{\frac{\left(1 - x \cdot x\right) \cdot \left(x + 1\right)}{x + 1}}$

# Runtime

Time bar (total: 29.6s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x)
:name "sqrt((1-x)*(1+x))"
(sqrt (* (- 1 x) (+ 1 x))))