Details

sample415.0ms

Algorithm

intervals

Results

65.0ms	250×	body	10240	exit
14.0ms	452×	body	80	nan
7.0ms	232×	body	80	valid
2.0ms	26×	body	160	valid

simplify70.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2626	7
7	5001	7
done	5001	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.2b	(- (exp (* 2.0 x)) 1.0)
5.4b	(- (exp x) 1.0)

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

29.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
43.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
12.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series207.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
62.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify119.0ms

Counts

135 → 135

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4287	1301
3	5003	1293
done	5003	1293

prune340.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.4b	(- (exp x) 1.0)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
11×	`sqrt-prod` `add-log-exp`
5×	`pow1` `add-cube-cbrt` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube`
3×	`sqrt-pow1` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `exp-prod` `exp-to-pow` `flip3-+` `pow1/2` `sum-log` `flip-+`

Counts

4 → 60

Calls

4 calls:

3.0ms	(sqrt (exp (* 2.0 x)))
17.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
17.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series132.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (exp (* 2.0 x)))
46.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
48.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
16.0ms	(- (exp x) 1.0)

simplify116.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	209	434
1	530	405
2	1324	402
3	3833	401
4	5001	401
done	5001	401

prune226.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x (+ 1.0 (* 0.5 x))) 2.0)
0.0b	(* x (+ 1.0 (* 0.5 x)))
24.0b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-r` `associate-l` `sqrt-prod` `flip-+`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `sqrt-div` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

11.0ms	(+ (* x (+ 1.0 (* 0.5 x))) 2.0)
18.0ms	(* x (+ 1.0 (* 0.5 x)))
14.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series168.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (* x (+ 1.0 (* 0.5 x))) 2.0)
64.0ms	(* x (+ 1.0 (* 0.5 x)))
79.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify42.0ms

Counts

59 → 59

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	308	385
1	1305	364
2	5001	352
done	5001	352

prune108.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes25.0ms

Accuracy

99.4% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 3.2b

bsearch63.0ms

Steps

Iters	Range		Point
6	2.0156653836354806e-07	1.163867227605777e-06	3.9558468439485187e-07
6	-2.6323548345885542e-05	-5.599255928070541e-06	-1.582886078662358e-05

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	22
1	41	22
done	41	22

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	6673×	body	10240	exit
376.0ms	12678×	body	80	nan
236.0ms	7440×	body	80	valid
52.0ms	696×	body	160	valid