Details

Time bar (total: 11.3s)

sample170.0ms

Algorithm
intervals
Results
108.0ms797×body80nan
37.0ms256×body80valid

simplify13.0ms

Counts
1 → 1
Iterations
IterNodes
318
218
114
09

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity
37×times-frac
34×add-sqr-sqrt
28×sqrt-prod
25×add-cube-cbrt
10×difference-of-squares
8×distribute-lft-out associate-/l*
7×div-inv
5×add-cbrt-cube add-exp-log add-log-exp
4×pow1 sqrt-div
3×associate-/r* distribute-rgt-out insert-posit16
2×flip3-- flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp frac-add distribute-rgt1-in flip-+
Counts
3 → 93
Calls
3 calls:
9.0ms
(/ (sqrt (- 1 (* x x))) x)
15.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
4.0ms
(sqrt (- 1 (* x x)))

series336.0ms

Counts
3 → 9
Calls
3 calls:
142.0ms
(/ (sqrt (- 1 (* x x))) x)
117.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
77.0ms
(sqrt (- 1 (* x x)))

simplify1.1s

Counts
102 → 102
Iterations
IterNodes
32987
2990
1379
0183

prune888.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
49×times-frac
48×log-pow
44×add-sqr-sqrt
40×exp-prod
37×add-cube-cbrt
30×sqrt-prod
13×pow1
12×associate-/l* difference-of-squares
8×distribute-lft-out
7×div-inv
6×add-cbrt-cube add-exp-log add-log-exp
4×insert-posit16
3×log-prod associate-/r* distribute-rgt-out
2×sqrt-div
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 flip3-+ flip3-- pow1/2 div-exp rem-log-exp frac-add distribute-rgt1-in flip-+ flip--
Counts
4 → 128
Calls
4 calls:
38.0ms
(/ (log (exp (sqrt (- 1 (* x x))))) x)
14.0ms
(log (exp (sqrt (- 1 (* x x)))))
4.0ms
(sqrt (- 1 (* x x)))
33.0ms
(+ (/ 1 x) (/ (log (exp (sqrt (- 1 (* x x))))) x))

series781.0ms

Counts
4 → 12
Calls
4 calls:
521.0ms
(/ (log (exp (sqrt (- 1 (* x x))))) x)
84.0ms
(log (exp (sqrt (- 1 (* x x)))))
75.0ms
(sqrt (- 1 (* x x)))
101.0ms
(+ (/ 1 x) (/ (log (exp (sqrt (- 1 (* x x))))) x))

simplify1.3s

Counts
140 → 140
Iterations
IterNodes
33276
21060
1431
0228

prune1.4s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations
IterNodes
214
114
011

end0.0ms

sample5.1s

Algorithm
intervals
Results
3.5s23694×body80nan
1.0s8000×body80valid