Details

sample151.0ms

Algorithm

intervals

Results

46.0ms	53×	body	1280	valid
28.0ms	25×	body	320	valid
25.0ms	41×	body	640	valid
20.0ms	127×	body	80	valid
3.0ms	10×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5042
7	2651
6	720
5	277
4	165
3	112
2	68
1	34
0	17

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (/ K 2.0)) J)
0.2b	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
7.4b	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
9.6b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite362.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
17×	`pow1`
16×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cbrt-cube`
12×	`add-cube-cbrt`
10×	`associate-l` `prod-exp`
8×	`sqrt-prod`
7×	`unpow-prod-down` `pow-prod-down` `cbrt-unprod`
4×	`sqrt-div` `associate-r` `pow-exp` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp`
2×	`flip3-+` `associate-l/` `-commutative` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `unswap-sqr` `sqr-pow`

Counts

4 → 85

Calls

4 calls:

7.0ms	(* (cos (/ K 2.0)) J)
17.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
238.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
98.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series788.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (cos (/ K 2.0)) J)
192.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
338.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
197.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify2.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1523
1	515
0	203

prune746.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.5b

localize91.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ K 2.0)))
0.4b	(cbrt (cos (/ K 2.0)))
7.4b	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* (cbrt (cos (/ K 2.0))) J)) -2.0))
9.6b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite680.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
29×	`add-exp-log`
23×	`add-cbrt-cube`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
13×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`sqrt-prod`
7×	`associate-l`
6×	`cbrt-prod`
4×	`sqrt-div` `add-log-exp`
2×	`flip3-+` `pow1/3` `associate-*l/` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 74

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
606.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* (cbrt (cos (/ K 2.0))) J)) -2.0))
70.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series947.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(cbrt (cos (/ K 2.0)))
197.0ms	(cbrt (cos (/ K 2.0)))
346.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* (cbrt (cos (/ K 2.0))) J)) -2.0))
199.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify2.5s

Counts

86 → 86

Iterations

Iter	Nodes
done	5004
2	1529
1	412
0	153

prune667.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.5b

localize121.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ K 2.0)))
0.4b	(cbrt (cos (/ K 2.0)))
7.4b	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (* (cbrt (cos (/ K 2.0))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (cbrt (cbrt (cos (/ K 2.0)))))) (* (cbrt (cos (/ K 2.0))) J)) -2.0))
9.6b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite4.7s

Algorithm

rewrite-expression-head

Rules

58×	`pow1`
57×	`add-exp-log`
43×	`pow-prod-down` `prod-exp` `cbrt-unprod`
39×	`add-cbrt-cube`
13×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`sqrt-prod`
7×	`associate-l`
6×	`cbrt-prod`
4×	`sqrt-div` `add-log-exp`
2×	`flip3-+` `pow1/3` `associate-*l/` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 86

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
4.6s	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (* (cbrt (cos (/ K 2.0))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (cbrt (cbrt (cos (/ K 2.0)))))) (* (cbrt (cos (/ K 2.0))) J)) -2.0))
85.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series988.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(cbrt (cos (/ K 2.0)))
200.0ms	(cbrt (cos (/ K 2.0)))
368.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (* (cbrt (cos (/ K 2.0))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (cbrt (cbrt (cos (/ K 2.0)))))) (* (cbrt (cos (/ K 2.0))) J)) -2.0))
209.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify2.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	2259
1	548
0	194

prune609.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.5b

localize102.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
7.4b	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
9.6b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
9.6b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `sqrt-pow1` `add-cube-cbrt`
6×	`rem-sqrt-square` `pow1/2`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

81.0ms	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
71.0ms	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
104.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
93.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

362.0ms	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
318.0ms	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
184.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
162.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify3.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	5025
4	4734
3	1421
2	465
1	195
0	97

prune778.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.5b

regimes997.0ms

Accuracy

4.1% (9.3b remaining)

Error of 18.1b against oracle of 8.8b and baseline of 18.5b

bsearch300.0ms

Steps

Iters	Range		Point
6	1.9402420999172678e-152	2.1045007062624737e-151	5.176467849961619e-152
8	-5.914036740599517e-58	-9.546406927973676e-63	-9.697315888830237e-63

simplify29.0ms

Iterations

Iter	Nodes
done	57
1	57
0	43

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.7s	1451×	body	1280	valid
1.2s	1263×	body	640	valid
776.0ms	4322×	body	80	valid
236.0ms	622×	body	320	valid
94.0ms	342×	body	160	valid