Details

Time bar (total: 10.4s)

sample91.0ms

Algorithm
intervals
Results
44.0ms821×body80nan
16.0ms256×body80valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0913
11213
21613
31813
done1813

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

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)

rewrite74.0ms

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:
50.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
18.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series319.0ms

Counts
2 → 6
Calls
2 calls:
156.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
163.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify2.1s

Counts
85 → 85
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01561177
13421087
28801032
325771023
done50011019

prune315.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
22×times-frac
20×*-un-lft-identity
18×add-cube-cbrt
13×fma-def associate-*r*
11×add-exp-log
8×sqrt-div
7×associate-*l* sqrt-prod add-cbrt-cube
6×frac-add unswap-sqr
4×pow1 frac-times flip3-- associate-*l/ prod-exp flip-- add-log-exp
3×div-inv
2×expm1-log1p-u associate-*r/ div-exp un-div-inv cbrt-unprod log1p-expm1-u
1×cbrt-undiv +-commutative rec-exp distribute-rgt-out flip3-+ 1-exp pow-prod-down sum-log *-commutative flip-+ difference-of-squares
Counts
2 → 82
Calls
2 calls:
24.0ms
(+ (/ 1.0 x) (* (sqrt (- 1.0 (* x x))) (/ 1 x)))
31.0ms
(* (sqrt (- 1.0 (* x x))) (/ 1 x))

series359.0ms

Counts
2 → 6
Calls
2 calls:
162.0ms
(+ (/ 1.0 x) (* (sqrt (- 1.0 (* x x))) (/ 1 x)))
197.0ms
(* (sqrt (- 1.0 (* x x))) (/ 1 x))

simplify2.8s

Counts
88 → 88
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01831399
14711144
213171032
341021013
done50001005

prune412.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11515
done1515

end0.0ms

sample3.8s

Algorithm
intervals
Results
2.3s23838×body80nan
751.0ms8000×body80valid