Details

Time bar (total: 4.7s)

sample43.0ms

Algorithm
intervals
Results
12.0ms263×body160nan
10.0ms503×body80nan
7.0ms256×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
1109
2119
done119

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
30.0b
(sqrt (- (* x x) 1.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity
4×sqrt-prod add-log-exp
3×pow1 add-cube-cbrt
2×add-exp-log sqrt-div add-cbrt-cube
1×+-commutative rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 sum-log flip-- flip-+ distribute-lft-out difference-of-squares
Counts
2 → 28
Calls
2 calls:
9.0ms
(+ x (sqrt (- (* x x) 1.0)))
5.0ms
(sqrt (- (* x x) 1.0))

series122.0ms

Counts
2 → 6
Calls
2 calls:
68.0ms
(+ x (sqrt (- (* x x) 1.0)))
54.0ms
(sqrt (- (* x x) 1.0))

simplify1.0s

Counts
34 → 34
Iterations

Useful iterations: 3 (305.0ms)

IterNodesCost
091451
1216402
2538366
31740358
done5000358

prune109.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×sqrt-prod
12×sqrt-div
10×*-un-lft-identity
9×associate-*r*
7×associate-*l*
6×pow1 add-cube-cbrt
4×add-exp-log frac-times flip3-+ add-cbrt-cube flip-+ add-log-exp unswap-sqr
3×flip3-- pow-prod-down flip--
2×sqrt-pow1 pow1/2 associate-*r/ associate-*l/ difference-of-squares
1×+-commutative sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
2 → 53
Calls
2 calls:
2.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
30.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series344.0ms

Counts
2 → 6
Calls
2 calls:
148.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
196.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify1.6s

Counts
59 → 59
Iterations

Useful iterations: 3 (836.0ms)

IterNodesCost
01521150
1360964
21012924
33584904
done5000904

prune167.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01014
11314
done1314

end0.0ms

sample1.2s

Algorithm
intervals
Results
344.0ms7630×body160nan
321.0ms16028×body80nan
221.0ms8000×body80valid