Details

sample326.0ms

Algorithm

intervals

Results

105.0ms	87×	body	1280	valid
85.0ms	92×	body	640	valid
54.0ms	233×	body	80	valid
20.0ms	52×	body	320	valid
9.0ms	33×	body	160	valid

simplify7.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	3421
6	1042
5	368
4	183
3	80
2	41
1	23
0	14

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize53.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.8b	(- (exp l) (exp (- l)))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`associate-r`
6×	`add-cube-cbrt`
5×	`add-log-exp`
4×	`associate-r/` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sub-neg` `flip3--` `flip--`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

3 → 60

Calls

3 calls:

91.0ms	(* J (- (exp l) (exp (- l))))
125.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
29.0ms	(- (exp l) (exp (- l)))

series352.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(* J (- (exp l) (exp (- l))))
173.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
68.0ms	(- (exp l) (exp (- l)))

simplify5.8s

Counts

69 → 69

Iterations

Iter	Nodes
done	5001
3	3797
2	871
1	284
0	114

prune723.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b	(* l (+ (* (* l l) 1/3) 2))
0.1b	(* 1/60 (pow l 5))
0.1b	(* (* J (+ (* l (+ (* (* l l) 1/3) 2)) (* 1/60 (pow l 5)))) (cos (/ K 2.0)))
0.2b	(* (* l l) 1/3)

rewrite534.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
19×	`add-sqr-sqrt`
18×	`add-cbrt-cube`
16×	`pow1` `associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`prod-exp`
8×	`associate-l` `cbrt-unprod`
7×	`pow-prod-down`
5×	`unswap-sqr`
4×	`unpow-prod-down` `associate-r/` `-commutative` `add-log-exp`
2×	`flip3-+` `associate-*l/` `flip-+` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-exp`

Counts

4 → 86

Calls

4 calls:

162.0ms	(* l (+ (* (* l l) 1/3) 2))
24.0ms	(* 1/60 (pow l 5))
305.0ms	(* (* J (+ (* l (+ (* (* l l) 1/3) 2)) (* 1/60 (pow l 5)))) (cos (/ K 2.0)))
38.0ms	(* (* l l) 1/3)

series696.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(* l (+ (* (* l l) 1/3) 2))
103.0ms	(* 1/60 (pow l 5))
356.0ms	(* (* J (+ (* l (+ (* (* l l) 1/3) 2)) (* 1/60 (pow l 5)))) (cos (/ K 2.0)))
52.0ms	(* (* l l) 1/3)

simplify3.3s

Counts

98 → 98

Iterations

Iter	Nodes
done	5028
2	2018
1	542
0	181

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/60 (pow l 5))
0.1b	(* J (* (+ (* l (+ (* (* l l) 1/3) 2)) (* 1/60 (pow l 5))) (cos (/ K 2.0))))
0.1b	(* (+ (* l (+ (* (* l l) 1/3) 2)) (* 1/60 (pow l 5))) (cos (/ K 2.0)))
0.2b	(* (* l l) 1/3)

rewrite541.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
19×	`add-sqr-sqrt`
18×	`add-cbrt-cube`
16×	`pow1`
14×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l` `prod-exp`
8×	`cbrt-unprod`
7×	`pow-prod-down`
5×	`unswap-sqr`
4×	`unpow-prod-down` `associate-l/` `-commutative` `add-log-exp`
2×	`flip3-+` `associate-*r/` `flip-+` `sqr-pow`
1×	`pow-to-exp` `pow-exp`

Counts

4 → 84

Calls

4 calls:

24.0ms	(* 1/60 (pow l 5))
257.0ms	(* J (* (+ (* l (+ (* (* l l) 1/3) 2)) (* 1/60 (pow l 5))) (cos (/ K 2.0))))
209.0ms	(* (+ (* l (+ (* (* l l) 1/3) 2)) (* 1/60 (pow l 5))) (cos (/ K 2.0)))
39.0ms	(* (* l l) 1/3)

series683.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* 1/60 (pow l 5))
322.0ms	(* J (* (+ (* l (+ (* (* l l) 1/3) 2)) (* 1/60 (pow l 5))) (cos (/ K 2.0))))
178.0ms	(* (+ (* l (+ (* (* l l) 1/3) 2)) (* 1/60 (pow l 5))) (cos (/ K 2.0)))
71.0ms	(* (* l l) 1/3)

simplify2.9s

Counts

96 → 96

Iterations

Iter	Nodes
done	5003
2	1528
1	454
0	172

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize101.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

23.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
2.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

560.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
292.0ms	(cbrt (cos (/ K 2.0)))
283.0ms	(cbrt (cos (/ K 2.0)))
288.0ms	(cbrt (cos (/ K 2.0)))

simplify4.0s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
4	2112
3	742
2	310
1	152
0	70

prune996.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes1.0s

Accuracy

57% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.4b

bsearch154.0ms

Steps

Iters	Range		Point
8	0.0008799215500326209	0.6307682633451466	0.015305213737446437

simplify15.0ms

Iterations

Iter	Nodes
done	45
1	45
0	33

end0.0ms

sample10.4s

Algorithm

intervals

Results

4.7s	2707×	body	1280	valid
2.1s	2588×	body	640	valid
1.4s	8329×	body	80	valid
826.0ms	1438×	body	320	valid
317.0ms	750×	body	160	valid