Details

sample229.0ms

Algorithm

intervals

Results

52.0ms	50×	body	1280	valid
27.0ms	40×	body	640	valid
21.0ms	135×	body	80	valid
10.0ms	21×	body	320	valid
3.0ms	10×	body	160	valid

simplify71.0ms

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	37	15
done	37	15

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

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))

rewrite76.0ms

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:

15.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
4.0ms	(- 1.0 (* (tan x) (tan x)))
13.0ms	(* (tan x) (tan x))
25.0ms	(* (tan x) (tan x))

series320.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
53.0ms	(- 1.0 (* (tan x) (tan x)))
62.0ms	(* (tan x) (tan x))
54.0ms	(* (tan x) (tan x))

simplify928.0ms

Counts

117 → 117

Iterations

Useful iterations: done (921.0ms)

Iter	Nodes	Cost
0	138	1632
1	350	1506
2	1540	1368
done	5001	1360

prune514.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

8.0ms	(- 1.0 (* (tan x) (tan x)))
34.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
12.0ms	(* (tan x) (tan x))
12.0ms	(* (tan x) (tan x))

series311.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- 1.0 (* (tan x) (tan x)))
145.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
63.0ms	(* (tan x) (tan x))
63.0ms	(* (tan x) (tan x))

simplify1.6s

Counts

177 → 177

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	249	3696
1	634	3313
2	2987	3110
done	5001	2894

prune443.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

5.0ms	(pow (cos x) 2)
5.0ms	(pow (cos x) 2)
6.0ms	(pow (sin x) 2)
7.0ms	(pow (sin x) 2)

series117.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (cos x) 2)
18.0ms	(pow (cos x) 2)
31.0ms	(pow (sin x) 2)
43.0ms	(pow (sin x) 2)

simplify1.0s

Counts

84 → 84

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	64	576
1	189	492
2	648	432
3	2402	432
done	5004	432

prune433.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

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	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-cbrt-cube` `add-exp-log`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp`
4×	`times-frac` `associate-/r/` `difference-of-squares`
3×	`pow2` `frac-times` `pow-plus` `distribute-rgt-out--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 106

Calls

4 calls:

14.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))
72.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (tan x) (tan x))
59.0ms	(* (tan x) (tan x))
49.0ms	(* (tan x) (tan x))
223.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify658.0ms

Counts

118 → 118

Iterations

Useful iterations: done (653.0ms)

Iter	Nodes	Cost
0	118	1623
1	300	1455
2	1251	1306
done	5000	1293

prune405.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes481.0ms

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	11	23
1	12	23
done	12	23

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.5s	1466×	body	1280	valid
1.2s	1241×	body	640	valid
1.1s	4372×	body	80	valid
341.0ms	592×	body	320	valid
145.0ms	329×	body	160	valid