Details

sample373.0ms

Algorithm

intervals

Results

19.0ms	44×	body	1280	valid
12.0ms	44×	body	640	valid
9.0ms	141×	body	80	valid
3.0ms	15×	body	320	valid
2.0ms	12×	body	160	valid

simplify54.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	21	15
3	26	15
4	34	15
5	36	15
done	36	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

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

21.0ms	(/ (- 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))
18.0ms	(* (tan x) (tan x))

series215.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- 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))
46.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

117 → 117

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	138	1632
1	315	1486
2	861	1368
3	2678	1346
done	5001	1342

prune248.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin x) 2)
0.2b	(pow (sin x) 2)
0.2b	(pow (cos x) 2)
0.2b	(pow (cos 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 (sin x) 2)
3.0ms	(pow (sin x) 2)
3.0ms	(pow (cos x) 2)
3.0ms	(pow (cos x) 2)

series80.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin x) 2)
20.0ms	(pow (sin x) 2)
18.0ms	(pow (cos x) 2)
22.0ms	(pow (cos x) 2)

simplify1.9s

Counts

84 → 84

Iterations

Useful iterations: 4 (726.0ms)

Iter	Nodes	Cost
0	64	576
1	133	492
2	277	432
3	760	432
4	3670	424
done	5000	424

prune211.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

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:

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

series200.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
64.0ms	(/ (* (tan x) (sin x)) (cos x))
44.0ms	(* (tan x) (sin x))
36.0ms	(* (tan x) (tan x))

simplify930.0ms

Counts

95 → 95

Iterations

Useful iterations: done (927.0ms)

Iter	Nodes	Cost
0	134	997
1	289	912
2	954	816
done	5001	807

prune236.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (/ (* (tan x) (sin x)) (cos x))) (sqrt (/ (* (tan x) (sin x)) (cos x))))
0.2b	(* (tan x) (tan x))
13.7b	(sqrt (/ (* (tan x) (sin x)) (cos x)))
13.7b	(sqrt (/ (* (tan x) (sin x)) (cos x)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

48×	`sqrt-prod`
40×	`add-sqr-sqrt`
28×	`pow1`
24×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`swap-sqr`
13×	`associate-r` `associate-l`
10×	`sqrt-pow1` `pow1/2`
8×	`add-exp-log` `add-cbrt-cube`
6×	`sqrt-div` `pow-prod-up` `div-inv`
5×	`unswap-sqr`
4×	`tan-quot` `pow-prod-down` `pow-sqr` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`sqrt-unprod` `rem-square-sqrt`

Counts

4 → 128

Calls

4 calls:

39.0ms	(* (sqrt (/ (* (tan x) (sin x)) (cos x))) (sqrt (/ (* (tan x) (sin x)) (cos x))))
15.0ms	(* (tan x) (tan x))
5.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))
7.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sqrt (/ (* (tan x) (sin x)) (cos x))) (sqrt (/ (* (tan x) (sin x)) (cos x))))
35.0ms	(* (tan x) (tan x))
75.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))
79.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))

simplify1.4s

Counts

140 → 140

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	140	2218
1	240	1553
2	742	1427
3	2789	1361
done	5000	1336

prune345.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes211.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	15	29
done	15	29

end0.0ms

sample1.6s

Algorithm

intervals

Results

638.0ms	1486×	body	1280	valid
337.0ms	1208×	body	640	valid
249.0ms	4384×	body	80	valid
117.0ms	593×	body	320	valid
52.0ms	329×	body	160	valid