Details

Time bar (total: 11.7s)

sample81.0ms

Algorithm
intervals
Results
49.0ms720×body80nan
12.0ms256×body80valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done16
216
112
09

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 3 expressions with local error:

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

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
28×add-sqr-sqrt
27×times-frac
22×add-cube-cbrt
20×sqrt-prod
7×associate-/l*
5×add-cbrt-cube add-exp-log add-log-exp difference-of-squares
4×pow1 sqrt-div distribute-lft-out
3×associate-/r* div-inv
2×flip3-- flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 flip3-+ distribute-rgt-out pow1/2 div-exp frac-add flip-+
Counts
3 → 78
Calls
3 calls:
4.0ms
(sqrt (- 1.0 (* x x)))
41.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
10.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series381.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(sqrt (- 1.0 (* x x)))
123.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
183.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify2.8s

Counts
87 → 87
Iterations
IterNodes
done5001
34833
21202
1393
0175

prune437.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt x))
0.2b
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
0.2b
(/ 1 (sqrt x))
0.5b
(* (/ 1 (sqrt x)) (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))

rewrite353.0ms

Algorithm
rewrite-expression-head
Rules
116×times-frac
105×add-sqr-sqrt
102×*-un-lft-identity
95×sqrt-prod
82×add-cube-cbrt
22×associate-*l*
21×add-exp-log
18×associate-/r*
15×add-cbrt-cube
13×associate-*r* associate-/l*
9×distribute-lft-out
8×pow1
7×difference-of-squares
6×div-exp div-inv
5×unswap-sqr
4×cbrt-undiv prod-exp add-log-exp
3×frac-times clear-num frac-2neg associate-*r/ pow-flip
2×rec-exp flip3-+ sqrt-div 1-exp frac-add cbrt-unprod flip-+ associate-/l/
1×distribute-rgt-in sqrt-undiv distribute-lft-in sqrt-pow1 distribute-rgt-out flip3-- pow1/2 pow-prod-down associate-*l/ *-commutative flip-- inv-pow
Counts
4 → 218
Calls
4 calls:
5.0ms
(/ 1.0 (sqrt x))
12.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
7.0ms
(/ 1 (sqrt x))
322.0ms
(* (/ 1 (sqrt x)) (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))

series411.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ 1.0 (sqrt x))
74.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
46.0ms
(/ 1 (sqrt x))
249.0ms
(* (/ 1 (sqrt x)) (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))

simplify2.4s

Counts
230 → 230
Iterations
IterNodes
done5008
22685
1860
0316

prune1.1s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify4.0ms

Iterations
IterNodes
done17
117
013

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.8s24045×body80nan
1.1s8000×body80valid