Details

sample1.1s

Algorithm

intervals

Results

778.0ms	239×	body	10240	exit
38.0ms	435×	body	80	nan
22.0ms	237×	body	80	valid
5.0ms	26×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	752
5	179
4	74
3	40
2	28
1	19
0	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.3b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.6b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (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-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`associate-/r/`
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 → 123

Calls

4 calls:

40.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
29.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
17.0ms	(- (exp (* 2.0 x)) 1.0)
11.0ms	(- (exp x) 1.0)

series261.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
113.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
33.0ms	(- (exp (* 2.0 x)) 1.0)
32.0ms	(- (exp x) 1.0)

simplify1.2s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
2	1218
1	396
0	189

prune713.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.3b	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
5.7b	(- (exp x) 1.0)
5.7b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite247.0ms

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*`
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 → 381

Calls

4 calls:

50.0ms	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
115.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
16.0ms	(- (exp x) 1.0)
33.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series717.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
408.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
18.0ms	(- (exp x) 1.0)
71.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify2.7s

Counts

393 → 393

Iterations

Iter	Nodes
done	5000
1	1248
0	570

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt (sqrt (exp (* 2.0 x))))
0.3b	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (* (/ (+ (sqrt (exp x)) (sqrt 1.0)) (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))) (/ (- (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))))))
5.8b	(- (sqrt (exp x)) (sqrt 1.0))
5.8b	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

54×	`sqrt-prod`
37×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
13×	`difference-of-squares`
9×	`sqrt-pow1` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1`
5×	`times-frac` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-exp-log`
3×	`rem-sqrt-square` `pow1/2` `associate-/r/`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`frac-times` `exp-prod` `exp-to-pow` `sqrt-div` `associate-l/` `associate-r/` `div-inv`

Counts

4 → 86

Calls

4 calls:

6.0ms	(sqrt (sqrt (exp (* 2.0 x))))
127.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (* (/ (+ (sqrt (exp x)) (sqrt 1.0)) (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))) (/ (- (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))))))
22.0ms	(- (sqrt (exp x)) (sqrt 1.0))
20.0ms	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

series2.1s

Counts

4 → 12

Calls

4 calls:

177.0ms	(sqrt (sqrt (exp (* 2.0 x))))
1.7s	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (* (/ (+ (sqrt (exp x)) (sqrt 1.0)) (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))) (/ (- (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))))))
47.0ms	(- (sqrt (exp x)) (sqrt 1.0))
218.0ms	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

simplify2.7s

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
2	2409
1	626
0	264

prune697.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize122.0ms

Local error

Found 4 expressions with local error:

5.8b	(- (sqrt (exp x)) (sqrt 1.0))
5.8b	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
5.8b	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
5.8b	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

78×	`sqrt-prod`
66×	`add-sqr-sqrt`
31×	`difference-of-squares`
26×	`*-un-lft-identity`
12×	`add-log-exp`
11×	`distribute-lft-out--`
4×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `flip--`

Counts

4 → 90

Calls

4 calls:

23.0ms	(- (sqrt (exp x)) (sqrt 1.0))
20.0ms	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
26.0ms	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
20.0ms	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

series809.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (sqrt (exp x)) (sqrt 1.0))
253.0ms	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
244.0ms	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))
247.0ms	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

simplify2.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
4	4634
3	1323
2	431
1	169
0	82

prune619.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes51.0ms

Accuracy

71% (0.9b remaining)

Error of 1.0b against oracle of 0.1b and baseline of 3.1b

bsearch103.0ms

Steps

Iters	Range		Point
8	-9.928957309417622e-14	-8.267506052856706e-17	-9.587317954112347e-14

simplify10.0ms

Iterations

Iter	Nodes
done	48
1	48
0	37

end0.0ms

sample6.9s

Algorithm

intervals

Results

4.4s	6921×	body	10240	exit
1.2s	12816×	body	80	nan
602.0ms	7380×	body	80	valid
172.0ms	732×	body	160	valid