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

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

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))))