Details

Time bar (total: 2.6s)

sample45.0ms

Algorithm
intervals
Results
20.0ms680×body80nan
9.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0913
11213
21613
done1613

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
33×times-frac
32×add-sqr-sqrt
26×add-cube-cbrt
20×sqrt-prod
8×log-prod distribute-lft-out
7×add-exp-log associate-/l*
6×pow1 add-cbrt-cube add-log-exp
5×div-inv difference-of-squares
4×sqrt-div
3×log-div associate-/r*
2×distribute-rgt-out flip3-- flip3-+ frac-add flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp clear-num sum-log log-pow
Counts
4 → 98
Calls
4 calls:
5.0ms
(sqrt (- 1.0 (* x x)))
22.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
24.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series578.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(sqrt (- 1.0 (* x x)))
290.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
125.0ms
(/ (sqrt (- 1.0 (* x x))) x)
101.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify455.0ms

Counts
110 → 110
Iterations

Useful iterations: done (451.0ms)

IterNodesCost
02261924
15131800
215211665
done50001652

prune280.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.2b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.2b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
24×times-frac
16×add-sqr-sqrt sqrt-prod distribute-lft-out
14×add-cube-cbrt
8×div-inv add-log-exp
6×pow1 sqrt-div
4×add-exp-log distribute-rgt-out flip3-+ frac-add add-cbrt-cube flip-+
2×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 76
Calls
4 calls:
23.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
25.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
42.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
45.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series616.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
102.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
201.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
206.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify371.0ms

Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
01641926
13931794
211481660