Details

Time bar (total: 10.3s)

sample106.0ms

Algorithm
intervals
Results
59.0ms821×body80nan
16.0ms256×body80valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0913
11213
21613
31813
done1813

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
35×*-un-lft-identity
31×add-sqr-sqrt
27×add-cube-cbrt
16×sqrt-prod
13×fma-def
7×associate-/l*
4×add-exp-log add-cbrt-cube div-inv distribute-lft-out add-log-exp difference-of-squares
3×associate-/r*
2×pow1 expm1-log1p-u sqrt-div log1p-expm1-u associate-/l/
1×cbrt-undiv +-commutative distribute-rgt-out flip3-- frac-2neg flip3-+ div-exp frac-add clear-num sum-log flip-- flip-+
Counts
2 → 79
Calls
2 calls:
55.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
13.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series277.0ms

Counts
2 → 6
Calls
2 calls:
133.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
144.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify2.2s

Counts
85 → 85
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01561177
13421087
28801032
325771023
done50011019

prune337.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
13×associate-*l*
12×*-un-lft-identity
11×times-frac
10×add-exp-log
9×add-cube-cbrt
6×add-cbrt-cube
4×associate-*r* prod-exp
3×pow1 unswap-sqr
2×frac-times flip3-+ associate-*r/ div-exp cbrt-unprod flip-+
1×cbrt-undiv distribute-rgt-in expm1-log1p-u rec-exp distribute-lft-in 1-exp pow-prod-down associate-*l/ *-commutative log1p-expm1-u div-inv distribute-lft-out add-log-exp
Counts
1 → 44
Calls
1 calls:
77.0ms
(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

series161.0ms

Counts
1 → 3
Calls
1 calls:
161.0ms
(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

simplify2.7s

Counts
47 → 47
Iterations

Useful iterations: done (2.7s)

IterNodesCost
0120816
1378698
21111606
33390605
done5000601

prune196.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11413
done1413

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.7s23838×body80nan
717.0ms8000×body80valid