Average Error: 13.5 → 13.5
Time: 14.1s
Precision: 64
Internal Precision: 3392
\[\sqrt{\frac{\sqrt{a^2 + b^2}^* + a}{2}}\]
\[\sqrt{\frac{a + \sqrt{a^2 + b^2}^*}{2}}\]

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.5

    \[\sqrt{\frac{\sqrt{a^2 + b^2}^* + a}{2}}\]
  2. Final simplification13.5

    \[\leadsto \sqrt{\frac{a + \sqrt{a^2 + b^2}^*}{2}}\]

Runtime

Time bar (total: 14.1s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (a b)
  :name "sqrt((hypot(a,b)+a)/2)"
  (sqrt (/ (+ (hypot a b) a) 2)))