Details

sample353.0ms

Algorithm

intervals

Results

23.0ms	48×	body	1280	valid
11.0ms	40×	body	640	valid
8.0ms	133×	body	80	valid
4.0ms	22×	body	320	valid
2.0ms	13×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9
done	37	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
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` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

22.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- 1.0 (* (tan x) (tan x)))
15.0ms	(* (tan x) (tan x))
17.0ms	(* (tan x) (tan x))

series218.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
39.0ms	(- 1.0 (* (tan x) (tan x)))
34.0ms	(* (tan x) (tan x))
48.0ms	(* (tan x) (tan x))

simplify43.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5001	824
done	5001	824

prune252.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(* (tan x) (sin x))
0.2b	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
0.3b	(* (tan x) (tan x))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

15.0ms	(/ (* (tan x) (sin x)) (cos x))
13.0ms	(* (tan x) (sin x))
9.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
18.0ms	(* (tan x) (tan x))

series197.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (* (tan x) (sin x)) (cos x))
47.0ms	(* (tan x) (sin x))
52.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
37.0ms	(* (tan x) (tan x))

simplify45.0ms

Counts

95 → 95

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	291	567
1	1265	503
2	5002	495
done	5002	495

prune260.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 2)
0.3b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

3.0ms	(pow (cos x) 2)
3.0ms	(pow (cos x) 2)
3.0ms	(pow (sin x) 2)
4.0ms	(pow (sin x) 2)

series78.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)
23.0ms	(pow (sin x) 2)
20.0ms	(pow (sin x) 2)

simplify60.0ms

Counts

84 → 84

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	141	284
1	469	240
2	1590	240
3	5001	236
done	5001	236

prune228.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1.0 (* (tan x) (tan x))))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.5b	(pow (* (tan x) (tan x)) 3)

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

236×	`tan-quot`
137×	`associate-*r/`
130×	`pow1`
97×	`frac-times`
78×	`associate-*l/`
45×	`frac-sub`
38×	`pow-prod-up`
25×	`pow-prod-down`
24×	`pow-sqr`
21×	`add-exp-log` `add-cbrt-cube`
20×	`pow-plus`
15×	`pow2`
14×	`sub-div`
11×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow-pow` `add-log-exp`
4×	`swap-sqr` `associate-r` `associate-l`
3×	`cube-div` `pow-unpow`
2×	`pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `flip3--` `distribute-rgt-out--` `diff-log` `unpow3` `cube-prod` `flip--` `sqr-pow`

Counts

4 → 207

Calls

4 calls:

15.0ms	(* (tan x) (tan x))
117.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1.0 (* (tan x) (tan x))))
70.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
12.0ms	(pow (* (tan x) (tan x)) 3)

series263.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (tan x) (tan x))
105.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1.0 (* (tan x) (tan x))))
48.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
72.0ms	(pow (* (tan x) (tan x)) 3)

simplify101.0ms

Counts

219 → 219

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	805	1700
1	3060	1367
2	5001	1356
done	5001	1356

prune346.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes225.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	26
1	20	26
done	20	26

end0.0ms

sample1.6s

Algorithm

intervals

Results

676.0ms	1533×	body	1280	valid
353.0ms	1249×	body	640	valid
260.0ms	4322×	body	80	valid
123.0ms	599×	body	320	valid
40.0ms	297×	body	160	valid