Details

Time bar (total: 5.9s)

sample102.0ms

Algorithm
intervals
Results
33.0ms273×body160nan
23.0ms575×body80nan
14.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
done12
212
111
07

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize17.0ms

Local error

Found 1 expressions with local error:

28.7b
(sqrt (- (* x x) 1.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt sqrt-prod
pow1 *-un-lft-identity sqrt-div add-cube-cbrt
expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-- add-cbrt-cube pow1/2 add-exp-log log1p-expm1-u flip-- add-log-exp difference-of-squares
Counts
1 → 18
Calls
1 calls:
16.0ms
(sqrt (- (* x x) 1.0))

series73.0ms

Counts
1 → 3
Calls
1 calls:
73.0ms
(sqrt (- (* x x) 1.0))

simplify832.0ms

Counts
21 → 21
Iterations
IterNodes
done5000
2638
1158
066

prune79.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x (sqrt 1.0)))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×sqrt-prod
14×sqrt-div
13×*-un-lft-identity
associate-*r*
pow1 associate-*l* add-cube-cbrt
frac-times flip3-+ add-cbrt-cube add-exp-log flip-+ unswap-sqr
sqrt-pow1 flip3-- pow1/2 pow-prod-down flip--
expm1-log1p-u associate-*l/ associate-*r/ hypot-def log1p-expm1-u distribute-lft-out add-log-exp difference-of-squares
rem-sqrt-square sqrt-unprod prod-exp *-commutative cbrt-unprod distribute-lft-out--
Counts
2 → 64
Calls
2 calls:
14.0ms
(sqrt (+ x (sqrt 1.0)))
50.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series302.0ms

Counts
2 → 6
Calls
2 calls:
74.0ms
(sqrt (+ x (sqrt 1.0)))
228.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify1.0s

Counts
70 → 70
Iterations
IterNodes
done5001
21350
1361
0154

prune309.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations
IterNodes
done13
113
010

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s15820×body80nan
652.0ms7642×body160nan
492.0ms8000×body80valid