Details

sample209.0ms

Algorithm

intervals

Results

137.0ms	105×	body	2560	valid
44.0ms	81×	body	1280	valid
8.0ms	34×	body	640	valid
4.0ms	25×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	11	4
2	11	4
done	11	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.7b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.2b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`times-frac`
12×	`add-cube-cbrt`
5×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`pow1`
1×	`tan-quot` `cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `frac-sub` `flip--`

Counts

2 → 50

Calls

2 calls:

6.0ms	(/ 1.0 (tan x))
27.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series148.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ 1.0 (tan x))
112.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify52.0ms

Counts

56 → 56

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	232	342
1	610	327
2	1894	327
3	5001	326
done	5001	326

prune119.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

9.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
11.0ms	(* 0.0021164021164021165 (pow x 5))
15.0ms	(* 0.022222222222222223 (pow x 3))

series230.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
53.0ms	(* 0.0021164021164021165 (pow x 5))
38.0ms	(* 0.022222222222222223 (pow x 3))

simplify40.0ms

Counts

76 → 76

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	282	308
1	1177	281
2	5001	281
done	5001	281

prune166.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

rewrite72.0ms

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:

52.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

series3.9s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
916.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
913.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
928.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

simplify59.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	480	1634
1	1767	1548
2	5001	1352
done	5001	1352

prune403.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.7b	(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
0.7b	(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
0.7b	(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

62×	`cbrt-div`
19×	`flip3-+` `flip-+`
12×	`frac-times`
6×	`cbrt-prod` `associate-r/` `associate-l/`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

6.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
22.0ms	(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
22.0ms	(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
25.0ms	(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))

series4.5s

Counts

4 → 12

Calls

4 calls:

936.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.2s	(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
1.2s	(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
1.2s	(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))

simplify53.0ms

Counts

76 → 76

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	453	1909
1	1490	1802
2	5001	1683
done	5001	1683

prune372.0ms

Pruning

19 alts after pruning (16 fresh and 3 done)

Merged error: 0.1b

regimes100.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	7
1	18	7
done	18	7

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.5s	3196×	body	2560	valid
1.4s	2474×	body	1280	valid
347.0ms	1343×	body	640	valid
120.0ms	624×	body	320	valid
93.0ms	8000×	pre	80	true
38.0ms	325×	body	160	valid
2.0ms	38×	body	80	valid