Details

sample237.0ms

Algorithm

intervals

Results

62.0ms	58×	body	1280	valid
24.0ms	35×	body	640	valid
19.0ms	141×	body	80	valid
7.0ms	16×	body	320	valid
2.0ms	6×	body	160	valid

simplify61.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	7	257
1	13	257
2	21	257
3	26	257
4	34	257
5	36	257
done	36	257

prune48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
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 → 105

Calls

4 calls:

7.0ms	(- 1.0 (* (tan x) (tan x)))
17.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
15.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))

series320.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- 1.0 (* (tan x) (tan x)))
163.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
58.0ms	(* (tan x) (tan x))
46.0ms	(* (tan x) (tan x))

simplify3.7s

Counts

117 → 117

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	138	38292
1	349	31966
2	996	31584
3	3680	31144
done	5033	31144

prune742.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (sin x) (tan x)) (cos x))
0.2b	(* (sin x) (tan x))
0.2b	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

25.0ms	(/ (* (sin x) (tan x)) (cos x))
12.0ms	(* (sin x) (tan x))
47.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
15.0ms	(* (tan x) (tan x))

series426.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (* (sin x) (tan x)) (cos x))
63.0ms	(* (sin x) (tan x))
194.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
69.0ms	(* (tan x) (tan x))

simplify2.1s

Counts

121 → 121

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	190	52871
1	486	47455
2	1536	46982
done	5000	46342

prune836.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos x) (* (sin x) (tan x)))
0.2b	(/ (- 1.0 (/ 1 (/ (cos x) (* (sin x) (tan x))))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(/ 1 (/ (cos x) (* (sin x) (tan x))))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

71×	`times-frac`
70×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
40×	`add-cube-cbrt`
34×	`add-exp-log`
22×	`add-cbrt-cube`
15×	`div-exp`
14×	`associate-/l*`
12×	`pow1` `associate-/r*` `difference-of-squares`
11×	`div-inv`
9×	`tan-quot`
8×	`cbrt-undiv` `associate-/r/` `distribute-lft-out--`
6×	`associate-*r/`
5×	`prod-exp`
4×	`add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `swap-sqr` `associate-r` `associate-l` `cbrt-unprod`
2×	`associate-/l/`
1×	`pow2` `frac-times` `flip3-+` `pow-plus` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `pow-sqr` `-commutative` `pow-prod-up` `flip-+` `pow-flip` `flip--` `inv-pow` `unswap-sqr`

Counts

4 → 162

Calls

4 calls:

15.0ms	(/ (cos x) (* (sin x) (tan x)))
128.0ms	(/ (- 1.0 (/ 1 (/ (cos x) (* (sin x) (tan x))))) (+ 1.0 (* (tan x) (tan x))))
26.0ms	(* (tan x) (tan x))
33.0ms	(/ 1 (/ (cos x) (* (sin x) (tan x))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (cos x) (* (sin x) (tan x)))
179.0ms	(/ (- 1.0 (/ 1 (/ (cos x) (* (sin x) (tan x))))) (+ 1.0 (* (tan x) (tan x))))
54.0ms	(* (tan x) (tan x))
90.0ms	(/ 1 (/ (cos x) (* (sin x) (tan x))))

simplify284.0ms

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	268	90177