Details

Time bar (total: 8.3s)

sample105.0ms

Algorithm
intervals
Results
38.0ms274×body160nan
24.0ms524×body80nan
14.0ms256×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1109
2119
done119

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize15.0ms

Local error

Found 1 expressions with local error:

31.7b
(sqrt (- (* x x) 1.0))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt sqrt-prod
pow1 add-cube-cbrt *-un-lft-identity sqrt-div
add-exp-log rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp difference-of-squares
Counts
1 → 16
Calls
1 calls:
21.0ms
(sqrt (- (* x x) 1.0))

series112.0ms

Counts
1 → 3
Calls
1 calls:
111.0ms
(sqrt (- (* x x) 1.0))

simplify1.6s

Counts
19 → 19
Iterations

Useful iterations: done (1.6s)

IterNodesCost
064227
1140199
2346185
31088185
done5000182

prune65.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×sqrt-prod
12×sqrt-div
*-un-lft-identity associate-*r*
associate-*l*
pow1 add-cube-cbrt
frac-times unswap-sqr
add-exp-log flip3-- flip3-+ pow-prod-down add-cbrt-cube flip-- flip-+
sqrt-pow1 pow1/2 associate-*r/ associate-*l/ difference-of-squares
sqrt-unprod prod-exp *-commutative cbrt-unprod distribute-lft-out distribute-lft-out-- add-log-exp
Counts
1 → 42
Calls
1 calls:
65.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series307.0ms

Counts
1 → 3
Calls
1 calls:
307.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify2.3s

Counts
45 → 45
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
0126833
1276702
2734686
32399674
done5000674

prune169.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01014
11314
done1314

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.5s16728×body80nan
796.0ms7880×body160nan
627.0ms8000×body80valid