Details

sample34.0ms

Algorithm

intervals

Results

16.0ms	84×	body	1280	valid
4.0ms	198×	body	80	valid
4.0ms	37×	body	640	valid
1.0ms	24×	body	320	valid
1.0ms	14×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	26	6
4	49	6
5	107	6
6	260	6
7	743	6
8	2493	6
done	5000	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.4b	(- (exp (* a x)) 1.0)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

1.0ms	(exp (* a x))
4.0ms	(- (exp (* a x)) 1.0)

series47.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
35.0ms	(- (exp (* a x)) 1.0)

simplify3.0s

Counts

30 → 30

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	53	263
1	116	248
2	312	232
3	1006	228
4	4468	226
done	5000	226

prune79.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* 2 (* x a)))
0.0b	(/ (- (exp (* 2 (* x a))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
3.4b	(- (exp (* 2 (* x a))) (* 1.0 1.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
16×	`times-frac`
14×	`add-cube-cbrt`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`distribute-lft-out`
4×	`pow1` `associate-/r` `associate-/l`
2×	`exp-prod` `flip3--` `exp-to-pow` `associate-/r/` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 74

Calls

4 calls:

1.0ms	(exp (* a x))
2.0ms	(exp (* 2 (* x a)))
28.0ms	(/ (- (exp (* 2 (* x a))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
6.0ms	(- (exp (* 2 (* x a))) (* 1.0 1.0))

series142.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(exp (* a x))
17.0ms	(exp (* 2 (* x a)))
61.0ms	(/ (- (exp (* 2 (* x a))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
47.0ms	(- (exp (* 2 (* x a))) (* 1.0 1.0))

simplify1.8s

Counts

86 → 86

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	136	1625
1	339	1565
2	932	1449
3	3373	1411
done	5000	1410

prune222.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (exp (* 2 (* x a))) (* 1.0 1.0)))
0.0b	(/ (/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (exp (* 2 (* x a))) (* 1.0 1.0))) (+ (exp (* a x)) 1.0))
0.0b	(exp (* (* a x) 4))
3.4b	(- (exp (* (* a x) 4)) (pow 1.0 4))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
199×	`add-sqr-sqrt`
195×	`*-un-lft-identity`
99×	`add-cube-cbrt`
60×	`difference-of-squares`
34×	`associate-/l*`
28×	`distribute-lft-out`
20×	`unpow-prod-down` `distribute-lft-out--` `sqr-pow`
14×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3-+` `associate-/r*` `flip-+` `div-inv`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `exp-prod` `exp-to-pow` `diff-log` `rem-exp-log`

Counts

4 → 231

Calls

4 calls:

20.0ms	(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (exp (* 2 (* x a))) (* 1.0 1.0)))
34.0ms	(/ (/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (exp (* 2 (* x a))) (* 1.0 1.0))) (+ (exp (* a x)) 1.0))
2.0ms	(exp (* (* a x) 4))
8.0ms	(- (exp (* (* a x) 4)) (pow 1.0 4))

series230.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (exp (* 2 (* x a))) (* 1.0 1.0)))
95.0ms	(/ (/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (exp (* 2 (* x a))) (* 1.0 1.0))) (+ (exp (* a x)) 1.0))
17.0ms	(exp (* (* a x) 4))
49.0ms	(- (exp (* (* a x) 4)) (pow 1.0 4))

simplify1.1s

Counts

243 → 243

Iterations

Useful iterations: 2 (495.0ms)

Iter	Nodes	Cost
0	362	10342
1	932	10011
2	2872	9626
done	5001	9626

prune851.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (* a x) 4))
0.0b	(exp (* (* a x) 4))
0.0b	(exp (* (* a x) 4))
3.3b	(- (* (exp (* (* a x) 4)) (exp (* (* a x) 4))) (* (pow 1.0 4) (pow 1.0 4)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`exp-prod` `exp-to-pow` `rem-exp-log`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 43

Calls

4 calls:

2.0ms	(exp (* (* a x) 4))
2.0ms	(exp (* (* a x) 4))
2.0ms	(exp (* (* a x) 4))
6.0ms	(- (* (exp (* (* a x) 4)) (exp (* (* a x) 4))) (* (pow 1.0 4) (pow 1.0 4)))

series112.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(exp (* (* a x) 4))
17.0ms	(exp (* (* a x) 4))
18.0ms	(exp (* (* a x) 4))
59.0ms	(- (* (exp (* (* a x) 4)) (exp (* (* a x) 4))) (* (pow 1.0 4) (pow 1.0 4)))

simplify1.4s

Counts

55 → 55

Iterations

Useful iterations: 3 (385.0ms)

Iter	Nodes	Cost
0	65	787
1	176	591
2	594	496
3	2756	478
done	5001	478

prune197.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

regimes120.0ms

Accuracy

62.5% (9.5b remaining)

Error of 13.7b against oracle of 4.2b and baseline of 29.6b

bsearch127.0ms

Steps

Iters	Range		Point
11	1.2907170496906384e+102	4.530903372306731e+124	1.3521665352267168e+102
8	-2.2623457567027846e+42	-3.641950481783047e+38	-1.1958856342471646e+42

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	116
1	66	116
done	66	116

end0.0ms

sample919.0ms

Algorithm

intervals

Results

420.0ms	2674×	body	1280	valid
137.0ms	1331×	body	640	valid
111.0ms	5485×	body	80	valid
47.0ms	717×	body	320	valid
19.0ms	431×	body	160	valid