Details

sample497.0ms

Algorithm

intervals

Results

158.0ms	51×	body	1280	valid
98.0ms	34×	body	640	valid
44.0ms	147×	body	80	valid
10.0ms	11×	body	320	valid
8.0ms	13×	body	160	valid

simplify65.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	46
6	46
5	44
4	39
3	31
2	24
1	15
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize58.0ms

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))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
24×	`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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `fma-neg` `prod-diff`
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 → 128

Calls

4 calls:

39.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
9.0ms	(- 1 (* (tan x) (tan x)))
28.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

series253.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
42.0ms	(- 1 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
73.0ms	(* (tan x) (tan x))

simplify3.2s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
3	4053
2	1038
1	401
0	157

prune632.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

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))))

rewrite397.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`*-commutative` `unswap-sqr`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `fma-neg` `diff-log` `prod-diff` `flip--`

Counts

4 → 270

Calls

4 calls:

14.0ms	(* (tan x) (tan x))
119.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
94.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
162.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))

series309.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (tan x) (tan x))
70.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
65.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
129.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))

simplify2.5s

Counts

282 → 282

Iterations

Iter	Nodes
done	5001
2	2524
1	939
0	263

prune889.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

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))))))

rewrite1.4m

Algorithm

rewrite-expression-head

Rules

2284968×	`tan-quot`
1378170×	`frac-times`
765456×	`associate-*r/`
761674×	`associate-*l/`
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×	`expm1-log1p-u` `sub-neg` `swap-sqr` `associate-r` `associate-l` `prod-diff` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`fma-neg` `diff-log`
1×	`cbrt-prod` `pow2` `pow-plus` `pow1/3` `cube-unmult` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `cbrt-unprod` `unswap-sqr`

Counts

4 → 242374

Calls

4 calls:

133.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))
166.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))
1.2s	(* (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
6.7s	(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))))))

series498.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))
116.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x)))
123.0ms	(* (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
160.0ms	(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	485205
0	485205