Details

Time bar (total: 11.1s)

sample146.0ms

Algorithm
intervals
Results
84.0ms813×body80nan
20.0ms256×body80valid

simplify13.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0913
11213
21613
done1613

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 1 expressions with local error:

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

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
6×times-frac
4×distribute-lft-out
3×add-sqr-sqrt add-cube-cbrt add-log-exp
2×div-inv
1×pow1 add-exp-log +-commutative distribute-rgt-out flip3-+ frac-add sum-log add-cbrt-cube flip-+
Counts
1 → 17
Calls
1 calls:
75.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series169.0ms

Counts
1 → 3
Calls
1 calls:
169.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify887.0ms

Counts
20 → 20
Iterations

Useful iterations: done (885.0ms)

IterNodesCost
069376
1177366
2655330
done5000319

prune152.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.1b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.1b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.4b
(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

rewrite795.0ms

Algorithm
rewrite-expression-head
Rules
90×*-un-lft-identity
58×sqrt-prod
42×add-sqr-sqrt times-frac
30×sqrt-div distribute-lft-out
28×add-cube-cbrt
21×pow1
15×swap-sqr
14×div-inv
11×flip3-+ associate-*r* associate-*l* frac-add flip-+
10×sqrt-pow1 pow1/2
9×frac-times
7×distribute-rgt-out
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-up
4×unswap-sqr
3×associate-*r/ pow-prod-down associate-*l/ pow-sqr
2×rem-sqrt-square
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 140
Calls
4 calls:
64.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
114.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
116.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
488.0ms
(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

series1.1s

Counts
4 → 12
Calls
4 calls:
167.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
318.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
334.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
272.0ms
(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

simplify2.3s

Counts
152 → 152
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02364553
15543442
225773177
done50013040

prune919.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01128
11228
done1228

end0.0ms

sample4.5s

Algorithm
intervals
Results
2.8s24078×body80nan
720.0ms8000×body80valid