Details

sample81.0ms

Algorithm

intervals

Results

22.0ms	129×	body	80	valid
21.0ms	51×	body	1280	valid
12.0ms	42×	body	640	valid
4.0ms	19×	body	320	valid
3.0ms	15×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	3510
6	440
5	117
4	53
3	30
2	22
1	15
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (pow (exp x) -2.0))
0.0b	(/ 2.0 (+ 1.0 (pow (exp x) -2.0)))
0.0b	(pow (exp x) -2.0)
3.4b	(- (/ 2.0 (+ 1.0 (pow (exp x) -2.0))) 1.0)

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
13×	`times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-lft-out`
4×	`associate-/r*` `pow-pow`
3×	`pow-unpow` `exp-prod` `unpow-prod-down` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+` `difference-of-squares`
1×	`pow-to-exp` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `pow-exp` `div-inv` `flip--` `distribute-lft-out--` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

8.0ms	(+ 1.0 (pow (exp x) -2.0))
18.0ms	(/ 2.0 (+ 1.0 (pow (exp x) -2.0)))
3.0ms	(pow (exp x) -2.0)
137.0ms	(- (/ 2.0 (+ 1.0 (pow (exp x) -2.0))) 1.0)

series662.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(+ 1.0 (pow (exp x) -2.0))
161.0ms	(/ 2.0 (+ 1.0 (pow (exp x) -2.0)))
153.0ms	(pow (exp x) -2.0)
234.0ms	(- (/ 2.0 (+ 1.0 (pow (exp x) -2.0))) 1.0)

simplify697.0ms

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	1156
1	347
0	148

prune491.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0))) (sqrt (+ 1.0 (pow (exp x) -2.0))))
0.0b	(pow (exp -2.0) x)
0.5b	(/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0)))
3.4b	(- (/ (/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0))) (sqrt (+ 1.0 (pow (exp x) -2.0)))) 1.0)

rewrite559.0ms

Algorithm

rewrite-expression-head

Rules

388×	`times-frac`
305×	`*-un-lft-identity`
229×	`sqrt-prod`
215×	`add-sqr-sqrt`
191×	`add-cube-cbrt`
56×	`distribute-lft-out`
30×	`associate-/l*`
20×	`sqrt-div` `associate-/r/`
14×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
10×	`flip3-+` `flip-+` `div-inv`
7×	`difference-of-squares`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `pow-pow` `div-exp`
3×	`pow-unpow` `exp-prod` `unpow-prod-down`
2×	`clear-num` `frac-2neg`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `flip--` `distribute-lft-out--` `sqr-pow` `associate-/l/`

Counts

4 → 325

Calls

4 calls:

83.0ms	(/ (/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0))) (sqrt (+ 1.0 (pow (exp x) -2.0))))
7.0ms	(pow (exp -2.0) x)
40.0ms	(/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0)))
394.0ms	(- (/ (/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0))) (sqrt (+ 1.0 (pow (exp x) -2.0)))) 1.0)

series684.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(/ (/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0))) (sqrt (+ 1.0 (pow (exp x) -2.0))))
29.0ms	(pow (exp -2.0) x)
102.0ms	(/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0)))
303.0ms	(- (/ (/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0))) (sqrt (+ 1.0 (pow (exp x) -2.0)))) 1.0)

simplify1.5s

Counts

337 → 337

Iterations

Iter	Nodes
done	5001
2	3665
1	960
0	407

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize88.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0)))
0.5b	(/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0)))
0.5b	(/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0)))
3.3b	(- (pow (/ (/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0))) (sqrt (+ (pow (exp x) -2.0) 1.0))) 3) (pow 1.0 3))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

240×	`add-sqr-sqrt`
143×	`times-frac`
88×	`sqrt-prod`
86×	`*-un-lft-identity`
64×	`difference-of-squares`
52×	`add-cube-cbrt`
48×	`unpow-prod-down` `cube-prod`
21×	`associate-/r*`
20×	`sqr-pow`
12×	`distribute-lft-out`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
6×	`sqrt-div` `associate-/r/` `add-log-exp`
5×	`distribute-lft-out--`
4×	`pow1`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 217

Calls

4 calls:

21.0ms	(/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0)))
23.0ms	(/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0)))
22.0ms	(/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0)))
1.7s	(- (pow (/ (/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0))) (sqrt (+ (pow (exp x) -2.0) 1.0))) 3) (pow 1.0 3))

series751.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0)))
121.0ms	(/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0)))
105.0ms	(/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0)))
426.0ms	(- (pow (/ (/ 2.0 (sqrt (+ (pow (exp -2.0) x) 1.0))) (sqrt (+ (pow (exp x) -2.0) 1.0))) 3) (pow 1.0 3))

simplify862.0ms

Counts

229 → 229

Iterations

Iter	Nodes
done	5000
2	1458
1	444
0	200

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize130.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 2.0 (sqrt (+ 1.0 (pow (exp x) -2.0))))
3.3b	(- (pow (/ (/ 2.0 (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt (+ (pow (exp x) -2.0) 1.0))) 3) (pow 1.0 3))
3.3b	(- (pow (/ (/ 2.0 (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt (+ (pow (exp x) -2.0) 1.0))) 3) (pow 1.0 3))
3.3b	(- (pow (/ (/ 2.0 (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt (+ (pow (exp x) -2.0) 1.0))) 3) (pow 1.0 3))

rewrite3.7s

Algorithm

rewrite-expression-head

Rules

584×	`add-sqr-sqrt`
261×	`times-frac`
192×	`difference-of-squares`
144×	`unpow-prod-down` `cube-prod`
136×	`sqrt-prod`
60×	`sqr-pow`
58×	`*-un-lft-identity`
20×	`add-cube-cbrt`
15×	`distribute-lft-out--`
10×	`add-log-exp`
7×	`associate-/r*`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `distribute-lft-out`
3×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`

Counts

4 → 291

Calls

4 calls:

26.0ms	(/ 2.0 (sqrt (+ 1.0 (pow (exp x) -2.0))))
1.3s	(- (pow (/ (/ 2.0 (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt (+ (pow (exp x) -2.0) 1.0))) 3) (pow 1.0 3))
1.2s	(- (pow (/ (/ 2.0 (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt (+ (pow (exp x) -2.0) 1.0))) 3) (pow 1.0 3))
1.2s	(- (pow (/ (/ 2.0 (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt (+ (pow (exp x) -2.0) 1.0))) 3) (pow 1.0 3))

series1.2s

Counts

4 → 12

Calls

4 calls:

240.0ms	(/ 2.0 (sqrt (+ 1.0 (pow (exp x) -2.0))))
344.0ms	(- (pow (/ (/ 2.0 (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt (+ (pow (exp x) -2.0) 1.0))) 3) (pow 1.0 3))
313.0ms	(- (pow (/ (/ 2.0 (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt (+ (pow (exp x) -2.0) 1.0))) 3) (pow 1.0 3))
266.0ms	(- (pow (/ (/ 2.0 (sqrt (+ 1.0 (pow (exp x) -2.0)))) (sqrt (+ (pow (exp x) -2.0) 1.0))) 3) (pow 1.0 3))

simplify591.0ms

Counts

303 → 303

Iterations

Iter	Nodes
done	5001
2	1353
1	411
0	189

prune2.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.7b

bsearch205.0ms

Steps

Iters	Range		Point
9	7.46228068957284e-06	5.1212688054922095	0.00093733924806542
9	-0.0007095347148853646	-6.590418748316962e-09	-0.0006697568994619957

simplify12.0ms

Iterations

Iter	Nodes
done	57
1	57
0	48

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	1627×	body	1280	valid
352.0ms	1289×	body	640	valid
236.0ms	4059×	body	80	valid
157.0ms	692×	body	320	valid
38.0ms	333×	body	160	valid