Details

sample210.0ms

Algorithm

intervals

Results

135.0ms	98×	body	2560	valid
46.0ms	88×	body	1280	valid
9.0ms	34×	body	640	valid
4.0ms	24×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.2b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.9b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite38.0ms

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:

9.0ms	(/ 1.0 (tan x))
27.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series144.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ 1.0 (tan x))
106.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify1.9s

Counts

56 → 56

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	115	619
1	234	592
2	497	566
3	1071	564
4	2824	562
done	5000	561

prune115.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

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` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

21.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
13.0ms	(* 0.0021164021164021165 (pow x 5))
13.0ms	(* 0.022222222222222223 (pow x 3))

series157.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
53.0ms	(* 0.0021164021164021165 (pow x 5))
38.0ms	(* 0.022222222222222223 (pow x 3))

simplify2.6s

Counts

78 → 78

Iterations

Useful iterations: 2 (135.0ms)

Iter	Nodes	Cost
0	123	847
1	301	764
2	965	708
3	4950	708
done	5000	708

prune170.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.022222222222222223 (pow x 3)) (+ (log (exp (* 0.0021164021164021165 (pow x 5)))) (* 0.3333333333333333 x)))
0.0b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))
0.6b	(log (exp (* 0.0021164021164021165 (pow x 5))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

27.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (log (exp (* 0.0021164021164021165 (pow x 5)))) (* 0.3333333333333333 x)))
14.0ms	(* 0.0021164021164021165 (pow x 5))
12.0ms	(* 0.022222222222222223 (pow x 3))
3.0ms	(log (exp (* 0.0021164021164021165 (pow x 5))))

series205.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (log (exp (* 0.0021164021164021165 (pow x 5)))) (* 0.3333333333333333 x)))
55.0ms	(* 0.0021164021164021165 (pow x 5))
37.0ms	(* 0.022222222222222223 (pow x 3))
53.0ms	(log (exp (* 0.0021164021164021165 (pow x 5))))

simplify2.7s

Counts

95 → 95

Iterations

Useful iterations: 2 (144.0ms)

Iter	Nodes	Cost
0	143	1042
1	322	888
2	990	820
3	4999	820
done	5001	820

prune228.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite184.0ms

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:

131.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
16.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
19.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
16.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

series1.2s

Counts

4 → 12

Calls

4 calls:

321.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
289.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
283.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
274.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

simplify700.0ms

Counts

99 → 99

Iterations

Useful iterations: done (694.0ms)

Iter	Nodes	Cost
0	196	4286
1	497	4035
2	1652	3736
done	5001	3214

prune376.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.2b

regimes74.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	17
1	20	17
done	20	17

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.5s	3285×	body	2560	valid
1.4s	2515×	body	1280	valid
364.0ms	1208×	body	640	valid
121.0ms	8000×	pre	80	true
110.0ms	617×	body	320	valid
41.0ms	332×	body	160	valid
3.0ms	43×	body	80	valid