Details

Time bar (total: 11.3s)

sample118.0ms

Algorithm
intervals
Results
62.0ms708×body80nan
19.0ms256×body80valid

simplify16.0ms

Counts
1 → 1
Iterations
IterNodes
done18
318
216
112
09

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity
27×times-frac
25×add-sqr-sqrt
21×add-cube-cbrt
16×sqrt-prod
8×log-prod
7×associate-/l*
5×add-exp-log
4×add-cbrt-cube distribute-lft-out difference-of-squares
3×pow1 log-div associate-/r* div-inv
2×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-+ distribute-rgt-out flip3-- div-exp rem-log-exp frac-add log-pow flip-+ flip--
Counts
2 → 69
Calls
2 calls:
21.0ms
(/ (sqrt (- 1.0 (* x x))) x)
30.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series684.0ms

Counts
2 → 6
Calls
2 calls:
211.0ms
(/ (sqrt (- 1.0 (* x x))) x)
473.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify1.6s

Counts
75 → 75
Iterations
IterNodes
done5001
21907
1463
0205

prune460.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
68×times-frac
58×*-un-lft-identity
52×sqrt-prod
42×add-cube-cbrt
14×associate-/l*
12×hypot-def
10×sqrt-div
8×add-cbrt-cube add-exp-log distribute-lft-out difference-of-squares
6×pow1 associate-/r* div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp associate-/l/
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-+ distribute-rgt-out flip3-- pow1/2 div-exp frac-add flip-+ flip--
Counts
4 → 152
Calls
4 calls:
14.0ms
(/ (sqrt (- 1.0 (* x x))) x)
19.0ms
(/ (sqrt (- 1.0 (* x x))) x)
77.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
68.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series982.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(/ (sqrt (- 1.0 (* x x))) x)
207.0ms
(/ (sqrt (- 1.0 (* x x))) x)
290.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
304.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify1.8s

Counts
164 → 164
Iterations
IterNodes
done5001
22015
1524
0231

prune1.2s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations
IterNodes
done12
112
011

end0.0ms

sample4.1s

Algorithm
intervals
Results
2.2s23956×body80nan
1.1s8000×body80valid