Details

sample417.0ms

Algorithm

intervals

Results

178.0ms	97×	body	2560	valid
111.0ms	723×	body	80	nan
60.0ms	65×	body	1280	valid
30.0ms	47×	body	640	valid
10.0ms	22×	body	320	valid
5.0ms	14×	body	160	valid
2.0ms	11×	body	80	valid

simplify700.0ms

Calls

1 calls:

Slowest

700.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize27.0ms

Local error

Found 2 expressions with local error:

26.7b	(pow (atan (fmod a (asin a))) (* a a))
2.2b	(fmod a (asin a))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow-unpow`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
3×	`pow1` `unpow-prod-down` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
2×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
1×	`pow-to-exp` `pow-pow` `pow-exp` `*-commutative` `unswap-sqr` `sqr-pow`

Calls

2 calls:

Slowest

8.0ms	(pow (atan (fmod a (asin a))) (* a a))
0.0ms	(fmod a (asin a))

series30.0ms

Calls

2 calls:

Slowest

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

simplify1.0s

Calls

23 calls:

Slowest

391.0ms	(+ (* 1/2 (* (pow a 4) (pow (log (atan (fmod a (asin a)))) 2))) (+ 1 (* (pow a 2) (log (atan (fmod a (asin a)))))))
354.0ms	(pow (* (cbrt (atan (fmod a (asin a)))) (cbrt (atan (fmod a (asin a))))) (* a a))
104.0ms	(pow (sqrt (atan (fmod a (asin a)))) (* a a))
54.0ms	(pow (atan (fmod a (asin a))) (pow a 2))
36.0ms	(pow (atan (fmod a (asin a))) (pow a 2))

prune441.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize12.0ms

Local error

Found 4 expressions with local error:

26.7b	(pow (atan (* (sqrt (fmod a (asin a))) (sqrt (fmod a (asin a))))) (* a a))
2.2b	(fmod a (asin a))
2.2b	(fmod a (asin a))
0.0b	(* (sqrt (fmod a (asin a))) (sqrt (fmod a (asin a))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
20×	`pow1`
18×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
15×	`pow-unpow`
11×	`swap-sqr`
9×	`associate-r` `associate-l`
8×	`sqrt-pow1` `pow1/2`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow-prod-up` `unswap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`unpow-prod-down` `pow-prod-down` `pow-sqr`
2×	`*-commutative`
1×	`pow2` `pow-to-exp` `rem-square-sqrt` `pow-pow` `pow-plus` `sqrt-unprod` `pow-exp` `prod-exp` `cbrt-unprod` `sqr-pow`

Calls

4 calls:

Slowest

8.0ms	(* (sqrt (fmod a (asin a))) (sqrt (fmod a (asin a))))
7.0ms	(pow (atan (* (sqrt (fmod a (asin a))) (sqrt (fmod a (asin a))))) (* a a))
0.0ms	(fmod a (asin a))
0.0ms	(fmod a (asin a))

series20.0ms

Calls

4 calls:

Slowest

15.0ms	(pow (atan (* (sqrt (fmod a (asin a))) (sqrt (fmod a (asin a))))) (* a a))
2.0ms	(* (sqrt (fmod a (asin a))) (sqrt (fmod a (asin a))))
2.0ms	(fmod a (asin a))
1.0ms	(fmod a (asin a))

simplify1.9s

Calls

89 calls:

Slowest

405.0ms	(+ (* 1/2 (* (pow a 4) (pow (log (atan (fmod a (asin a)))) 2))) (+ 1 (* (pow a 2) (log (atan (fmod a (asin a)))))))
320.0ms	(pow (sqrt (atan (* (sqrt (fmod a (asin a))) (sqrt (fmod a (asin a)))))) (* a a))
292.0ms	(pow (* (cbrt (atan (* (sqrt (fmod a (asin a))) (sqrt (fmod a (asin a)))))) (cbrt (atan (* (sqrt (fmod a (asin a))) (sqrt (fmod a (asin a))))))) (* a a))
159.0ms	(* (* (* (sqrt (fmod a (asin a))) (sqrt (fmod a (asin a)))) (sqrt (fmod a (asin a)))) (* (* (sqrt (fmod a (asin a))) (sqrt (fmod a (asin a)))) (sqrt (fmod a (asin a)))))
107.0ms	(* (* (cbrt (sqrt (fmod a (asin a)))) (cbrt (sqrt (fmod a (asin a))))) (* (cbrt (sqrt (fmod a (asin a)))) (cbrt (sqrt (fmod a (asin a))))))

prune1.3s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 33.3b

end0.0ms

sample13.4s

Algorithm

intervals

Results

5.0s	2912×	body	2560	valid
4.1s	23850×	body	80	nan
2.4s	2485×	body	1280	valid
969.0ms	1324×	body	640	valid
353.0ms	666×	body	320	valid
105.0ms	331×	body	160	valid
55.0ms	282×	body	80	valid