Details

sample324.0ms

Algorithm

intervals

Results

185.0ms	102×	body	2560	valid
68.0ms	81×	body	1280	valid
31.0ms	23×	body	320	valid
16.0ms	38×	body	640	valid
5.0ms	256×	pre	80	true
3.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.6b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.4b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite68.0ms

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))
58.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series185.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ 1.0 (tan x))
125.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify1.6s

Counts

56 → 56

Iterations

Useful iterations: 3 (768.0ms)

Iter	Nodes	Cost
0	115	619
1	242	592
2	685	566
3	3990	564
done	5000	564

prune162.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

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:

16.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
30.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
17.0ms	(* 0.0021164021164021165 (pow x 5))
23.0ms	(* 0.022222222222222223 (pow x 3))

series364.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
76.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
67.0ms	(* 0.0021164021164021165 (pow x 5))
63.0ms	(* 0.022222222222222223 (pow x 3))

simplify808.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (237.0ms)

Iter	Nodes	Cost
0	138	1055
1	384	935
2	1721	885
done	5002	885

prune236.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (log (exp (* 0.022222222222222223 (pow x 3)))) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))
2.2b	(log (exp (* 0.022222222222222223 (pow x 3))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

38.0ms	(+ (log (exp (* 0.022222222222222223 (pow x 3)))) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
21.0ms	(* 0.0021164021164021165 (pow x 5))
28.0ms	(* 0.022222222222222223 (pow x 3))
5.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (log (exp (* 0.022222222222222223 (pow x 3)))) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
62.0ms	(* 0.0021164021164021165 (pow x 5))
39.0ms	(* 0.022222222222222223 (pow x 3))
45.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))

simplify650.0ms

Counts

100 → 100

Iterations

Useful iterations: done (647.0ms)

Iter	Nodes	Cost
0	144	1127
1	358	963
2	1342	905
done	5000	903

prune312.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))
1.5b	(log (exp (* 0.0021164021164021165 (pow x 5))))
2.2b	(log (exp (* 0.022222222222222223 (pow x 3))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

25.0ms	(* 0.0021164021164021165 (pow x 5))
20.0ms	(* 0.022222222222222223 (pow x 3))
5.0ms	(log (exp (* 0.0021164021164021165 (pow x 5))))
5.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* 0.0021164021164021165 (pow x 5))
39.0ms	(* 0.022222222222222223 (pow x 3))
58.0ms	(log (exp (* 0.0021164021164021165 (pow x 5))))
41.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))

simplify496.0ms

Counts

96 → 96

Iterations

Useful iterations: done (494.0ms)

Iter	Nodes	Cost
0	129	798
1	273	676
2	916	624
done	5001	620

prune281.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

regimes32.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	19
1	22	19
done	22	19

end0.0ms

sample11.5s

Algorithm

intervals

Results

7.3s	3208×	body	2560	valid
2.4s	2467×	body	1280	valid
1.1s	1316×	body	640	valid
210.0ms	655×	body	320	valid
177.0ms	8000×	pre	80	true
68.0ms	308×	body	160	valid
5.0ms	46×	body	80	valid