Details

Time bar (total: 5.8s)

sample84.0ms

Algorithm
intervals
Results
21.0ms295×body160nan
21.0ms550×body80nan
11.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1109
2119
done119

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize7.0ms

Local error

Found 1 expressions with local error:

32.0b
(sqrt (- (* x x) 1.0))

rewrite11.0ms

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:
10.0ms
(sqrt (- (* x x) 1.0))

series62.0ms

Counts
1 → 3
Calls
1 calls:
62.0ms
(sqrt (- (* x x) 1.0))

simplify1.5s

Counts
19 → 19
Iterations

Useful iterations: done (1.5s)

IterNodesCost
064227
1140199
2346185
31088185
done5000182

prune89.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 1 expressions with local error:

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

rewrite107.0ms

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:
103.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series291.0ms

Counts
1 → 3
Calls
1 calls:
290.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify1.6s

Counts
45 → 45
Iterations

Useful iterations: 3 (637.0ms)

IterNodesCost
0126833
1276702
2734686
32399674
done5000674

prune109.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01014
11314
done1314

end0.0ms

sample1.9s

Algorithm
intervals
Results
465.0ms7681×body160nan
451.0ms16486×body80nan
297.0ms8000×body80valid