Details

Time bar (total: 7.9s)

sample122.0ms

Algorithm
intervals
Results
44.0ms530×body80nan
31.0ms256×body160nan
17.0ms256×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: 32.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
30.4b
(sqrt (- (* x x) 1.0))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt *-un-lft-identity
sqrt-prod add-log-exp
pow1 add-cube-cbrt
add-exp-log sqrt-div add-cbrt-cube
+-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:
22.0ms
(+ x (sqrt (- (* x x) 1.0)))
23.0ms
(sqrt (- (* x x) 1.0))

series167.0ms

Counts
2 → 6
Calls
2 calls:
97.0ms
(+ x (sqrt (- (* x x) 1.0)))
71.0ms
(sqrt (- (* x x) 1.0))

simplify1.7s

Counts
34 → 34
Iterations

Useful iterations: done (1.7s)

IterNodesCost
091451
1216402
2541366
31508358
done5001351

prune133.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ 0.125 (pow x 3))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down cube-prod associate-/r*
add-exp-log
cube-mult unpow3 sqr-pow
div-exp add-cbrt-cube associate-/l*
pow1 cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv add-log-exp
Counts
1 → 65
Calls
1 calls:
18.0ms
(/ 0.125 (pow x 3))

series73.0ms

Counts
1 → 3
Calls
1 calls:
73.0ms
(/ 0.125 (pow x 3))

simplify2.1s

Counts
68 → 68
Iterations

Useful iterations: 2 (148.0ms)

IterNodesCost
096728
1166584
2470568
32527568
done5000568

prune192.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
11314
done1314

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.1s16341×body80nan
849.0ms8000×body80valid
742.0ms7613×body160nan