Details

sample400.0ms

Algorithm

intervals

Results

161.0ms	97×	body	2560	valid
102.0ms	713×	body	80	nan
78.0ms	87×	body	1280	valid
24.0ms	37×	body	640	valid
7.0ms	16×	body	320	valid
3.0ms	9×	body	160	valid
2.0ms	10×	body	80	valid

simplify73.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

73.0ms

(pow (atan (fmod a (asin a))) (* a a))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize14.0ms

Local error

Found 2 expressions with local error:

29.9b	(pow (atan (fmod a (asin a))) (* a a))
2.4b	(fmod a (asin a))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `pow1` `unpow-prod-down` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
2×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 28

Calls

2 calls:

Slowest

3.0ms	(pow (atan (fmod a (asin a))) (* a a))
0.0ms	(fmod a (asin a))

series28.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

25.0ms	(pow (atan (fmod a (asin a))) (* a a))
3.0ms	(fmod a (asin a))

simplify3.8s

Counts

38 → 34

Calls

38 calls:

Slowest

618.0ms	(+ (* 1/2 (* (pow a 4) (pow (log (atan (fmod a (asin a)))) 2))) (+ 1 (* (pow a 2) (log (atan (fmod a (asin a)))))))
559.0ms	(* (* (pow (atan (fmod a (asin a))) (* a a)) (pow (atan (fmod a (asin a))) (* a a))) (pow (atan (fmod a (asin a))) (* a a)))
402.0ms	(* (cbrt (pow (atan (fmod a (asin a))) (* a a))) (cbrt (pow (atan (fmod a (asin a))) (* a a))))
369.0ms	(pow (* (cbrt (atan (fmod a (asin a)))) (cbrt (atan (fmod a (asin a))))) (* a a))
161.0ms	(log (pow (atan (fmod a (asin a))) (* a a)))

prune376.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize46.0ms

Local error

Found 4 expressions with local error:

29.9b	(pow (atan (* (* (cbrt (fmod a (asin a))) (cbrt (fmod a (asin a)))) (cbrt (fmod a (asin a))))) (* a a))
2.4b	(fmod a (asin a))
2.4b	(fmod a (asin a))
2.4b	(fmod a (asin a))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

4 → 48

Calls

4 calls:

Slowest

7.0ms	(pow (atan (* (* (cbrt (fmod a (asin a))) (cbrt (fmod a (asin a)))) (cbrt (fmod a (asin a))))) (* a a))
0.0ms	(fmod a (asin a))
0.0ms	(fmod a (asin a))
0.0ms	(fmod a (asin a))

series23.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

18.0ms	(pow (atan (* (* (cbrt (fmod a (asin a))) (cbrt (fmod a (asin a)))) (cbrt (fmod a (asin a))))) (* a a))
2.0ms	(fmod a (asin a))
2.0ms	(fmod a (asin a))
2.0ms	(fmod a (asin a))

simplify8.6s

Counts

64 → 60

Calls

64 calls:

Slowest

602.0ms	(pow (atan (* (* (cbrt (fmod a (asin a))) (cbrt (fmod a (asin a)))) (cbrt (fmod a (asin a))))) (/ (* a a) 2))
577.0ms	(* (* (pow (atan (* (* (cbrt (fmod a (asin a))) (cbrt (fmod a (asin a)))) (cbrt (fmod a (asin a))))) (* a a)) (pow (atan (* (* (cbrt (fmod a (asin a))) (cbrt (fmod a (asin a)))) (cbrt (fmod a (asin a))))) (* a a))) (pow (atan (* (* (cbrt (fmod a (asin a))) (cbrt (fmod a (asin a)))) (cbrt (fmod a (asin a))))) (* a a)))
557.0ms	(pow (atan (* (* (cbrt (fmod a (asin a))) (cbrt (fmod a (asin a)))) (cbrt (fmod a (asin a))))) (/ (* a a) 2))
542.0ms	(exp (pow (atan (* (* (cbrt (fmod a (asin a))) (cbrt (fmod a (asin a)))) (cbrt (fmod a (asin a))))) (* a a)))
518.0ms	(+ (* 1/2 (* (pow a 4) (pow (log (atan (fmod a (asin a)))) 2))) (+ 1 (* (pow a 2) (log (atan (fmod a (asin a)))))))

prune645.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 30.6b

end0.0ms

sample13.7s

Algorithm

intervals

Results

4.7s	23892×	body	80	nan
4.4s	3035×	body	2560	valid
2.3s	2490×	body	1280	valid
1.2s	1299×	body	640	valid
343.0ms	624×	body	320	valid
152.0ms	292×	body	160	valid
88.0ms	260×	body	80	valid