Details

sample245.0ms

Algorithm

intervals

Results

57.0ms	51×	body	1280	valid
26.0ms	147×	body	80	valid
26.0ms	34×	body	640	valid
6.0ms	11×	body	320	valid
5.0ms	13×	body	160	valid

simplify55.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	38
5	38
4	36
3	28
2	23
1	15
0	7

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.1b	(- 1 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`pow1`
15×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`associate-/l*`
4×	`insert-posit16`
3×	`associate-/r*`
2×	`pow2` `frac-times` `pow-plus` `flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 114

Calls

4 calls:

22.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
4.0ms	(- 1 (* (tan x) (tan x)))
16.0ms	(* (tan x) (tan x))
27.0ms	(* (tan x) (tan x))

series294.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
46.0ms	(- 1 (* (tan x) (tan x)))
47.0ms	(* (tan x) (tan x))
69.0ms	(* (tan x) (tan x))

simplify2.2s

Counts

126 → 126

Iterations

Iter	Nodes
done	5070
3	3113
2	964
1	376
0	144

prune494.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.3b	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))

rewrite400.0ms

Algorithm

rewrite-expression-head

Rules

264×	`tan-quot`
233×	`pow1`
147×	`associate-*r/`
113×	`frac-times`
88×	`associate-*l/`
73×	`pow-prod-up`
47×	`pow-prod-down`
45×	`pow-sqr` `frac-sub`
37×	`pow-plus`
30×	`add-cbrt-cube` `add-exp-log`
27×	`pow2`
17×	`prod-exp` `cbrt-unprod`
14×	`sub-div`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
5×	`swap-sqr` `associate-r` `associate-l`
4×	`insert-posit16`
3×	`*-commutative` `unswap-sqr`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `flip--`

Counts

4 → 260

Calls

4 calls:

24.0ms	(* (tan x) (tan x))
96.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
90.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
179.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))

series264.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (tan x) (tan x))
54.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
58.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
93.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))

simplify3.2s

Counts

272 → 272

Iterations

Iter	Nodes
done	5007
3	4611
2	1859
1	823
0	252

prune858.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))
0.3b	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))
0.3b	(* (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
10.5b	(cbrt (* (* (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))))

rewrite1.3m

Algorithm

rewrite-expression-head

Rules

2284968×	`tan-quot`
1378170×	`frac-times`
765456×	`associate-*l/`
761674×	`associate-*r/`
524610×	`frac-sub`
238327×	`cbrt-div`
163212×	`sub-div`
11658×	`flip3--` `flip--`
11×	`pow1`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
4×	`sub-neg` `swap-sqr` `associate-r` `associate-l` `insert-posit16`
2×	`distribute-rgt-in` `distribute-lft-in` `diff-log`
1×	`cbrt-prod` `pow2` `pow-plus` `pow1/3` `pow3` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `cbrt-unprod` `unswap-sqr`

Counts

4 → 242360

Calls

4 calls:

98.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))
99.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))
906.0ms	(* (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
6.4s	(cbrt (* (* (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))
92.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))
145.0ms	(* (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
111.0ms	(cbrt (* (* (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))))

simplify8.5m

Iterations

Iter	Nodes
done	485191
0	485191