Details

sample346.0ms

Algorithm

intervals

Results

142.0ms	208×	body	10240	exit
77.0ms	399×	body	80	nan
19.0ms	238×	body	80	valid
4.0ms	23×	body	160	valid

simplify9.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5043
8	4148
7	1069
6	332
5	133
4	65
3	37
2	27
1	19
0	10

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.8b

localize132.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.8b	(- (exp (* 2.0 x)) 1.0)
4.9b	(- (exp x) 1.0)

rewrite341.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`associate-/r/` `insert-posit16`
2×	`rem-sqrt-square` `sub-neg` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp`

Counts

4 → 127

Calls

4 calls:

139.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
121.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
34.0ms	(- (exp (* 2.0 x)) 1.0)
33.0ms	(- (exp x) 1.0)

series426.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
188.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
39.0ms	(- (exp (* 2.0 x)) 1.0)
37.0ms	(- (exp x) 1.0)

simplify6.3s

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
3	3362
2	1010
1	400
0	193

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize120.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.2b	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
4.9b	(- (exp x) 1.0)
4.9b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite594.0ms

Algorithm

rewrite-expression-head

Rules

591×	`*-un-lft-identity`
554×	`sqrt-prod`
528×	`times-frac`
521×	`add-sqr-sqrt`
184×	`difference-of-squares`
147×	`add-cube-cbrt`
120×	`distribute-lft-out--`
102×	`distribute-lft-out`
13×	`associate-/r/`
9×	`associate-/r*` `flip3--` `flip--`
8×	`add-log-exp`
7×	`div-inv`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/l*`
4×	`insert-posit16`
3×	`rem-sqrt-square`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp`

Counts

4 → 385

Calls

4 calls:

123.0ms	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
253.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
47.0ms	(- (exp x) 1.0)
43.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series982.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
590.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
31.0ms	(- (exp x) 1.0)
106.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify7.9s

Counts

397 → 397

Iterations

Iter	Nodes
done	5003
2	3590
1	1248
0	574

prune2.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize190.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.2b	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (posit16->real (real->posit16 (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))))
4.9b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.9b	(- (exp x) 1.0)

rewrite276.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
67×	`sqrt-prod`
61×	`times-frac`
39×	`difference-of-squares`
29×	`add-cube-cbrt`
25×	`distribute-lft-out--`
9×	`associate-/r*`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
5×	`pow1` `associate-/l*`
4×	`flip3--` `insert-posit16` `flip--`
2×	`rem-sqrt-square` `sub-neg` `diff-log` `associate-/r/` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp`

Counts

4 → 143

Calls

4 calls:

126.0ms	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
52.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (posit16->real (real->posit16 (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))))
62.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
23.0ms	(- (exp x) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

283.0ms	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
639.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (posit16->real (real->posit16 (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))))
81.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
34.0ms	(- (exp x) 1.0)

simplify5.1s

Counts

155 → 155

Iterations

Iter	Nodes
done	5001
2	1958
1	656
0	286

prune2.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize258.0ms

Local error

Found 4 expressions with local error:

4.9b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.9b	(- (exp x) 1.0)
4.9b	(- (exp x) 1.0)
4.9b	(- (exp x) 1.0)

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-log-exp`
7×	`difference-of-squares`
6×	`sqrt-prod`
5×	`distribute-lft-out--`
4×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `insert-posit16` `flip--`

Counts

4 → 64

Calls

4 calls:

44.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
30.0ms	(- (exp x) 1.0)
32.0ms	(- (exp x) 1.0)
47.0ms	(- (exp x) 1.0)

series132.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
20.0ms	(- (exp x) 1.0)
19.0ms	(- (exp x) 1.0)
21.0ms	(- (exp x) 1.0)

simplify4.6s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
4	2289
3	924
2	394
1	164
0	78

prune777.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes139.0ms

Accuracy

72.4% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.0b

bsearch110.0ms

Steps

Iters	Range		Point
6	-1.790535254998819e-16	-1.1589515176165432e-17	-1.6879468583117964e-16

simplify34.0ms

Iterations

Iter	Nodes
done	38
1	38
0	32

end0.0ms

sample8.5s

Algorithm

intervals

Results

5.2s	6697×	body	10240	exit
1.6s	12419×	body	80	nan
869.0ms	7394×	body	80	valid
142.0ms	732×	body	160	valid