Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	47×	body	1280	valid
4.0ms	30×	body	640	valid
4.0ms	141×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	12×	body	160	valid

simplify61.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	30	5
3	52	5
4	114	5
5	322	5
6	1627	5
7	5002	5
done	5002	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
4.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

6.0ms	(+ 1.0 (exp (* -2.0 x)))
13.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
66.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series135.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(+ 1.0 (exp (* -2.0 x)))
40.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
77.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify104.0ms

Counts

69 → 69

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	251	494
1	731	465
2	2785	460
3	5001	460
done	5001	460

prune136.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
4.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
4.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
4.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite578.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
32×	`cbrt-prod` `*-un-lft-identity`
14×	`difference-of-squares`
12×	`add-cube-cbrt` `cbrt-div`
11×	`pow1` `swap-sqr`
10×	`add-log-exp`
9×	`flip3--` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
7×	`times-frac`
6×	`add-exp-log` `pow1/3`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 104

Calls

4 calls:

239.0ms	(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
63.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
65.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
207.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series443.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
77.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
74.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
77.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify120.0ms

Counts

116 → 116

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	262	1573
1	815	1472
2	3983	1340
3	5002	1315
done	5002	1315

prune272.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (+ 1.0 (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (* 1.0 1.0)))) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
4.1b	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))
4.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
4.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite916.0ms

Algorithm

rewrite-expression-head

Rules

257×	`add-sqr-sqrt`
136×	`times-frac`
118×	`cbrt-prod`
108×	`associate-l`
102×	`difference-of-squares`
90×	`*-un-lft-identity`
72×	`unpow-prod-down` `cube-prod`
44×	`add-cube-cbrt`
40×	`sqr-pow`
23×	`distribute-lft-out--`
10×	`add-log-exp`
9×	`associate-r`
7×	`cbrt-div`
6×	`pow1` `add-exp-log` `unswap-sqr`
5×	`flip3--` `flip--`
4×	`difference-cubes` `add-cbrt-cube`
3×	`sub-neg` `diff-log`
2×	`frac-times` `pow1/3` `associate-*r/` `pow-prod-down` `associate-/r/`
1×	`flip3-+` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 212

Calls

4 calls:

611.0ms	(* (cbrt (/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (+ 1.0 (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (* 1.0 1.0)))) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
159.0ms	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))
64.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
65.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

850.0ms	(* (cbrt (/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (+ 1.0 (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (* 1.0 1.0)))) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
127.0ms	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))
78.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
78.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify93.0ms

Counts

224 → 224

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	760	5530
1	2037	5414
2	5001	5410
done	5001	5410

prune777.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
0.1b	(* 0.33333333333333337 (pow x 3))
0.2b	(* 5.551115123125783e-17 (pow x 4))
7.6b	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite51.0ms

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` `sqr-pow`
2×	`pow-to-exp` `diff-log` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `sub-neg` `flip3--` `flip3-+` `unpow3` `flip--` `flip-+` `associate--r+`

Counts

4 → 81

Calls

4 calls:

15.0ms	(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
14.0ms	(* 0.33333333333333337 (pow x 3))
11.0ms	(* 5.551115123125783e-17 (pow x 4))
9.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
36.0ms	(* 0.33333333333333337 (pow x 3))
42.0ms	(* 5.551115123125783e-17 (pow x 4))
107.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify51.0ms

Counts

93 → 93

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	344	493
1	1475	459
2	5001	459
done	5001	459

prune192.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes151.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 29.2b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	44
1	52	44
done	52	44

end0.0ms

sample899.0ms

Algorithm

intervals

Results

344.0ms	1695×	body	1280	valid
172.0ms	1270×	body	640	valid
114.0ms	4109×	body	80	valid
53.0ms	610×	body	320	valid
18.0ms	316×	body	160	valid