Details

sample210.0ms

Algorithm

intervals

Results

141.0ms	93×	body	2560	valid
43.0ms	92×	body	1280	valid
7.0ms	40×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	18×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	2×	body	80	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
2	11	8
done	11	8

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 59.9b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

2.6b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`times-frac`
5×	`distribute-lft-out--`
4×	`difference-of-squares`
3×	`add-cube-cbrt` `add-log-exp`
2×	`div-inv`
1×	`pow1` `add-exp-log` `sub-neg` `flip3--` `diff-log` `frac-sub` `add-cbrt-cube` `flip--`

Counts

1 → 22

Calls

1 calls:

15.0ms

(- (/ 1.0 x) (/ 1.0 (tan x)))

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify706.0ms

Counts

25 → 25

Iterations

Useful iterations: done (705.0ms)

Iter	Nodes	Cost
0	75	358
1	165	348
2	352	330
3	869	330
4	2613	328
done	5000	327

prune53.0ms

Filtered

21 candidates to 25 candidates (-19.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	24	1	25
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	1	26

Merged error: 0.3b

Counts

26 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))
0.0b	(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
0.0b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3`

Counts

4 → 80

Calls

4 calls:

7.0ms	(+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))
5.0ms	(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
6.0ms	(* 0.0021164021164021165 (pow x 5))
7.0ms	(* 0.022222222222222223 (pow x 3))

series32.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))
13.0ms	(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
8.0ms	(* 0.0021164021164021165 (pow x 5))
4.0ms	(* 0.022222222222222223 (pow x 3))

simplify422.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	136	1095
1	365	971
2	1219	921
done	5000	921

prune162.0ms

Filtered

59 candidates to 92 candidates (-55.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	87	6	93

Merged error: 0.2b

Counts

93 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))) (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))))
0.7b	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
0.7b	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
0.7b	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

19.0ms	(* (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))) (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))))
6.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
6.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
6.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))) (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))))
22.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
22.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
22.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))

simplify462.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (143.0ms)

Iter	Nodes	Cost
0	196	4286
1	497	4025
2	1831	3768
done	5000	3768

prune894.0ms

Filtered

77 candidates to 99 candidates (-28.6%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	88	11	99
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	88	17	105

Merged error: 0.1b

Counts

105 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
0.7b	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
0.7b	(cbrt (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))))
0.7b	(cbrt (* (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))) (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-div`
16×	`cbrt-prod`
9×	`flip3-+` `flip-+`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `frac-times` `pow1/3` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `associate-l/`

Counts

4 → 59

Calls

4 calls:

7.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
6.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
7.0ms	(cbrt (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))))
15.0ms	(cbrt (* (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))) (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))))

series104.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
22.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
27.0ms	(cbrt (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))))
33.0ms	(cbrt (* (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))) (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))))

simplify518.0ms

Counts

71 → 71

Iterations

Useful iterations: 2 (164.0ms)

Iter	Nodes	Cost
0	249	3360
1	605	3224
2	2030	3020
done	5001	3020

prune727.0ms

Filtered

63 candidates to 71 candidates (-12.7%)

Pruning

20 alts after pruning (17 fresh and 3 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	1	13	14
Picked	0	1	1
Done	0	2	2
Total	68	20	88

Merged error: 0.1b

Counts

88 → 20

regimes178.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	18	15
done	18	15

end0.0ms

sample7.1s

Algorithm

intervals

Results

5.2s	3271×	body	2560	valid
1.3s	2515×	body	1280	valid
225.0ms	1195×	body	640	valid
127.0ms	8000×	pre	80	true
77.0ms	617×	body	320	valid
30.0ms	356×	body	160	valid
2.0ms	46×	body	80	valid

Details

sample210.0ms

simplify3.0ms

prune7.0ms

localize5.0ms

rewrite16.0ms

series20.0ms

simplify706.0ms

prune53.0ms

localize10.0ms

rewrite27.0ms

series32.0ms

simplify422.0ms

prune162.0ms

localize15.0ms

rewrite41.0ms

series96.0ms

simplify462.0ms

prune894.0ms

localize21.0ms

rewrite37.0ms

series104.0ms

simplify518.0ms

prune727.0ms

regimes178.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample7.1s

Profiling