Details

sample215.0ms

Algorithm

intervals

Results

141.0ms	93×	body	2560	valid
48.0ms	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

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

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)))

series22.0ms

Counts

1 → 3

Calls

1 calls:

22.0ms

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

simplify641.0ms

Counts

25 → 25

Iterations

Useful iterations: 4 (250.0ms)

Iter	Nodes	Cost
0	75	358
1	165	348
2	352	330
3	826	330
4	2120	328
done	5001	328

prune47.0ms

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

localize13.0ms

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))

rewrite28.0ms

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))

series29.0ms

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)))
5.0ms	(* 0.0021164021164021165 (pow x 5))
4.0ms	(* 0.022222222222222223 (pow x 3))

simplify439.0ms

Counts

92 → 92

Iterations

Useful iterations: done (436.0ms)

Iter	Nodes	Cost
0	136	1095
1	365	983
2	1235	929
done	5000	927

prune173.0ms

Filtered

64 candidates to 92 candidates (-43.8%)

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)))))

rewrite44.0ms

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:

18.0ms	(* (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))))))
7.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
7.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))
9.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (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))))))
25.0ms	(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)))))
23.0ms	(cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))))

simplify487.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (134.0ms)

Iter	Nodes	Cost
0	196	4286
1	497	4040
2	1847	3768
done	5000	3768

prune665.0ms

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

localize23.0ms

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)))))))

rewrite39.0ms

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)))))
7.0ms	(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))))))
16.0ms	(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)))))))

series106.0ms

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))))))
35.0ms	(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)))))))

simplify507.0ms

Counts

71 → 71

Iterations

Useful iterations: 2 (152.0ms)

Iter	Nodes	Cost
0	249	3360
1	605	3224
2	2033	3020
done	5000	3020

prune765.0ms

Filtered

66 candidates to 71 candidates (-7.6%)

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

regimes181.0ms

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

sample7.2s

Algorithm

intervals

Results

5.2s	3271×	body	2560	valid
1.3s	2515×	body	1280	valid
230.0ms	1195×	body	640	valid
129.0ms	8000×	pre	80	true
74.0ms	617×	body	320	valid
33.0ms	356×	body	160	valid
2.0ms	46×	body	80	valid

Details

sample215.0ms

simplify4.0ms

prune2.0ms

localize5.0ms

rewrite16.0ms

series22.0ms

simplify641.0ms

prune47.0ms

localize13.0ms

rewrite28.0ms

series29.0ms

simplify439.0ms

prune173.0ms

localize15.0ms

rewrite44.0ms

series97.0ms

simplify487.0ms

prune665.0ms

localize23.0ms

rewrite39.0ms

series106.0ms

simplify507.0ms

prune765.0ms

regimes181.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample7.2s

Profiling