Details

sample420.0ms

Algorithm

intervals

Results

64.0ms	224×	body	10240	exit
14.0ms	425×	body	80	nan
8.0ms	235×	body	80	valid
2.0ms	27×	body	160	valid

simplify71.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 5.5b

localize11.0ms

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))
5.9b	(- (exp (* 2.0 x)) 1.0)
6.0b	(- (exp x) 1.0)

rewrite103.0ms

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:

28.0ms	(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)
13.0ms	(- (exp x) 1.0)

series197.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
60.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify117.0ms

Counts

135 → 135

Iterations

Useful iterations: 3 (105.0ms)

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

prune315.0ms

Pruning

3 alts after pruning (3 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)))
6.0b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
6.0b	(- (exp x) 1.0)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

3.0ms	(sqrt (exp (* 2.0 x)))
5.0ms	(sqrt (exp (* 2.0 x)))
17.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series107.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (exp (* 2.0 x)))
24.0ms	(sqrt (exp (* 2.0 x)))
46.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify101.0ms

Counts

74 → 74

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	168	382
1	414	365
2	1068	363
3	3163	361
4	5001	361
done	5001	361

prune215.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x)))))
6.0b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
6.0b	(- (exp x) 1.0)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

83×	`sqrt-pow1`
75×	`sqrt-prod`
58×	`add-sqr-sqrt`
28×	`pow1`
23×	`*-un-lft-identity`
21×	`add-log-exp`
17×	`add-cube-cbrt` `pow1/2`
15×	`swap-sqr`
13×	`exp-prod` `exp-to-pow` `pow-prod-up`
9×	`associate-r` `associate-l` `pow-prod-down` `pow-sqr` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`difference-of-squares`
3×	`distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

3.0ms	(sqrt (exp (* 2.0 x)))
32.0ms	(* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x)))))
20.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series108.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (exp (* 2.0 x)))
22.0ms	(* (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt (exp (* 2.0 x)))))
49.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify226.0ms

Counts

146 → 146

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	280	774
1	984	713
2	4935	689
3	5001	689
done	5001	689

prune307.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ 1.0 (* 0.5 x)))
28.8b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

15.0ms	(* x (+ 1.0 (* 0.5 x)))
16.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series136.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(* x (+ 1.0 (* 0.5 x)))
76.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify36.0ms

Counts

43 → 43

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	279	281
1	1132	268
2	5002	256
done	5002	256

prune73.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes22.0ms

Accuracy

77.6% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.3b

bsearch43.0ms

Steps

Iters	Range		Point
8	-0.001391736753177052	-2.391427350769765e-06	-1.0296566467916756e-05

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	22
1	35	22
done	35	22

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	6898×	body	10240	exit
402.0ms	12822×	body	80	nan
256.0ms	7407×	body	80	valid
58.0ms	730×	body	160	valid