Details

Time bar (total: 11.4s)

sample193.0ms

Algorithm
intervals
Results
105.0ms789×body80nan
61.0ms256×body80valid

simplify14.0ms

Counts
1 → 1
Iterations
IterNodes
done18
218
114
09

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite453.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
50×times-frac
43×add-sqr-sqrt
31×add-cube-cbrt sqrt-prod
16×distribute-lft-out
15×log-prod
13×div-inv
10×difference-of-squares
8×associate-/l*
7×add-exp-log
6×pow1 distribute-rgt-out add-cbrt-cube add-log-exp
4×sqrt-div insert-posit16
3×log-div associate-/r*
2×flip3-+ flip3-- frac-add distribute-rgt1-in flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp log-pow
Counts
4 → 121
Calls
4 calls:
18.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
9.0ms
(/ (sqrt (- 1 (* x x))) x)
389.0ms
(sqrt (- 1 (* x x)))
32.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

series515.0ms

Counts
4 → 12
Calls
4 calls:
226.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
148.0ms
(/ (sqrt (- 1 (* x x))) x)
47.0ms
(sqrt (- 1 (* x x)))
95.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

simplify1.4s

Counts
133 → 133
Iterations
IterNodes
done2000
32000
21397
1525
0239

prune1.2s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
0.0b
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
0.2b
(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
0.2b
(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
82×*-un-lft-identity
52×times-frac
42×sqrt-prod
36×add-sqr-sqrt
32×distribute-lft-out
24×div-inv
22×add-cube-cbrt
12×distribute-rgt-out
8×add-log-exp
6×pow1 sqrt-div
4×flip3-+ add-cbrt-cube frac-add distribute-rgt1-in add-exp-log flip-+ insert-posit16
2×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
4 → 108
Calls
4 calls:
22.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
17.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
33.0ms
(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
23.0ms
(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
71.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
135.0ms
(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
160.0ms
(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

simplify1.1s

Counts
120 → 120
Iterations
IterNodes
done2000
32000
2859
1317
0144

prune1.2s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations
IterNodes
done14
114
011

end0.0ms

sample4.7s

Algorithm
intervals
Results
3.2s23583×body80nan
975.0ms8000×body80valid