Details

sample235.0ms

Algorithm

intervals

Results

49.0ms	47×	body	1280	valid
30.0ms	40×	body	640	valid
19.0ms	138×	body	80	valid
9.0ms	19×	body	320	valid
4.0ms	12×	body	160	valid

simplify57.0ms

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	37	257
done	37	257

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize158.0ms

Local error

Found 4 expressions with local error:

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

rewrite228.0ms

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)))
51.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
19.0ms	(* (tan x) (tan x))
133.0ms	(* (tan x) (tan x))

series272.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- 1.0 (* (tan x) (tan x)))
114.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
51.0ms	(* (tan x) (tan x))
65.0ms	(* (tan x) (tan x))

simplify1.5s

Counts

117 → 117

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	138	38292
1	350	31966
2	1536	31264
done	5000	31184

prune578.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`add-cube-cbrt`
21×	`pow1` `associate-r` `add-exp-log`
20×	`times-frac`
15×	`add-cbrt-cube`
10×	`associate-l`
8×	`tan-quot`
6×	`swap-sqr` `prod-exp`
5×	`unswap-sqr`
4×	`frac-times` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`associate-/r` `pow-prod-down` `associate-r/` `-commutative` `associate-/l`
2×	`pow2` `cbrt-undiv` `rec-exp` `flip3-+` `pow-plus` `flip3--` `1-exp` `pow-sqr` `pow-prod-up` `flip-+` `div-inv` `flip--`
1×	`clear-num` `frac-2neg` `un-div-inv` `pow-flip` `inv-pow` `difference-of-squares`

Counts

4 → 132

Calls

4 calls:

15.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
55.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
27.0ms	(* (tan x) (tan x))
23.0ms	(* (tan x) (tan x))

series297.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
140.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
42.0ms	(* (tan x) (tan x))
49.0ms	(* (tan x) (tan x))

simplify3.2s

Counts

144 → 144

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	169	47772
1	442	38394
2	3121	36340
done	5000	36180

prune623.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1`
28×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
16×	`tan-quot`
12×	`add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `add-log-exp` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

12.0ms	(* (tan x) (tan x))
12.0ms	(* (tan x) (tan x))
12.0ms	(* (tan x) (tan x))
19.0ms	(* (tan x) (tan x))

series192.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))
43.0ms	(* (tan x) (tan x))
47.0ms	(* (tan x) (tan x))

simplify8.4s

Counts

124 → 124

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	49	28552
1	124	22048
2	563	21204
3	4667	21044
done	5000	21044

prune687.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1`
28×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
12×	`add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `tan-quot` `add-exp-log`
7×	`frac-times`
6×	`flip3-+` `flip-+`
5×	`associate-l/` `associate-r/`
4×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `add-log-exp` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 119

Calls

4 calls:

22.0ms	(* (+ 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
22.0ms	(* (tan x) (tan x))
20.0ms	(* (tan x) (tan x))
12.0ms	(* (tan x) (tan x))

series219.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (+ 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
42.0ms	(* (tan x) (tan x))
46.0ms	(* (tan x) (tan x))
60.0ms	(* (tan x) (tan x))

simplify1.7s

Counts

131 → 131

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	107	36890
1	344	28461
2	1933	27668
done	5002	27508

prune625.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes465.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	617
1	21	617
done	21	617

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.4s	1465×	body	1280	valid
1.2s	1308×	body	640	valid
598.0ms	598×	body	320	valid
474.0ms	4287×	body	80	valid
81.0ms	342×	body	160	valid