Details

sample453.0ms

Algorithm

intervals

Results

144.0ms	97×	body	2560	valid
120.0ms	87×	body	1280	valid
114.0ms	713×	body	80	nan
28.0ms	37×	body	640	valid
9.0ms	16×	body	320	valid
3.0ms	9×	body	160	valid
2.0ms	10×	body	80	valid

simplify89.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

89.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

Slowest

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

series31.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

28.0ms	(pow (atan (fmod a (asin a))) (* a a))
3.0ms	(fmod a (asin a))

simplify3.5s

Counts

34 → 30

Calls

34 calls:

Slowest

552.0ms	(* (* (pow (atan (fmod a (asin a))) (* a a)) (pow (atan (fmod a (asin a))) (* a a))) (pow (atan (fmod a (asin a))) (* a a)))
451.0ms	(+ (* 1/2 (* (pow a 4) (pow (log (atan (fmod a (asin a)))) 2))) (+ 1 (* (pow a 2) (log (atan (fmod a (asin a)))))))
364.0ms	(* (cbrt (pow (atan (fmod a (asin a))) (* a a))) (cbrt (pow (atan (fmod a (asin a))) (* a a))))
350.0ms	(pow (* (cbrt (atan (fmod a (asin a)))) (cbrt (atan (fmod a (asin a))))) (* a a))
200.0ms	(log (pow (atan (fmod a (asin a))) (* a a)))

prune331.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize29.0ms

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))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

Slowest

8.0ms	(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))

series49.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

40.0ms	(pow (atan (* (* (cbrt (fmod a (asin a))) (cbrt (fmod a (asin a)))) (cbrt (fmod a (asin a))))) (* a a))
3.0ms	(fmod a (asin a))
3.0ms	(fmod a (asin a))
3.0ms	(fmod a (asin a))

simplify8.0s

Counts

56 → 52

Calls

56 calls:

Slowest

598.0ms	(exp (pow (atan (* (* (cbrt (fmod a (asin a))) (cbrt (fmod a (asin a)))) (cbrt (fmod a (asin a))))) (* a a)))
590.0ms	(pow (atan (* (* (cbrt (fmod a (asin a))) (cbrt (fmod a (asin a)))) (cbrt (fmod a (asin a))))) (/ (* a a) 2))
587.0ms	(+ (* 1/2 (* (pow a 4) (pow (log (atan (fmod a (asin a)))) 2))) (+ 1 (* (pow a 2) (log (atan (fmod a (asin a)))))))
549.0ms	(* (* (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)))
473.0ms	(pow (cbrt (atan (* (* (cbrt (fmod a (asin a))) (cbrt (fmod a (asin a)))) (cbrt (fmod a (asin a)))))) (* a a))

prune669.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 30.6b

end0.0ms

sample15.1s

Algorithm

intervals

Results

5.4s	3035×	body	2560	valid
4.3s	23892×	body	80	nan
3.4s	2490×	body	1280	valid
885.0ms	1299×	body	640	valid
330.0ms	624×	body	320	valid
113.0ms	292×	body	160	valid
53.0ms	260×	body	80	valid