Details

Time bar (total: 5.7s)

sample72.0ms

Algorithm
intervals
Results
21.0ms546×body80nan
16.0ms244×body160nan
10.0ms256×body80valid

simplify16.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
31.9b
(sqrt (- (* x x) 1.0))

rewrite55.0ms

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:
35.0ms
(+ x (sqrt (- (* x x) 1.0)))
19.0ms
(sqrt (- (* x x) 1.0))

series153.0ms

Counts
2 → 6
Calls
2 calls:
72.0ms
(+ x (sqrt (- (* x x) 1.0)))
80.0ms
(sqrt (- (* x x) 1.0))

simplify795.0ms

Counts
34 → 34

prune116.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize12.0ms

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))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×sqrt-prod
12×sqrt-div
10×*-un-lft-identity
associate-*r*
associate-*l*
pow1 add-cube-cbrt
add-exp-log frac-times flip3-+ add-cbrt-cube flip-+ add-log-exp unswap-sqr
flip3-- pow-prod-down flip--
sqrt-pow1 pow1/2 associate-*r/ associate-*l/ difference-of-squares
+-commutative sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
2 → 53
Calls
2 calls:
6.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
61.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series412.0ms

Counts
2 → 6
Calls
2 calls:
185.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
227.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify565.0ms

Counts
59 → 59

prune235.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify28.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
876.0ms8000×body80valid
790.0ms7645×body160nan
763.0ms16401×body80nan