Details

sample103.0ms

Algorithm

intervals

Results

29.0ms	47×	body	1280	valid
18.0ms	147×	body	80	valid
16.0ms	34×	body	640	valid
5.0ms	17×	body	320	valid
3.0ms	11×	body	160	valid

simplify5.9s

Counts

1 → 1

Iterations

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

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (/ K 2.0)) J)
0.3b	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
8.8b	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
8.9b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite689.0ms

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` `insert-posit16` `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 → 89

Calls

4 calls:

13.0ms	(* (cos (/ K 2.0)) J)
58.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
463.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
150.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (cos (/ K 2.0)) J)
381.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
613.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
359.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify4.1s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	1532
1	525
0	207

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.5b

localize129.0ms

Local error

Found 4 expressions with local error:

8.8b	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
8.8b	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
8.9b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
8.9b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite652.0ms

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-+` `insert-posit16` `distribute-lft-out` `add-log-exp`

Counts

4 → 80

Calls

4 calls:

155.0ms	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
165.0ms	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
143.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
185.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

764.0ms	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
649.0ms	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
310.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
310.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify7.8s

Counts

92 → 92

Iterations

Iter	Nodes
done	5010
4	4777
3	1369
2	459
1	197
0	99

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.5b

localize145.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
8.8b	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
8.9b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
17.9b	(pow (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0) 1/4)

rewrite566.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`sqrt-prod`
15×	`add-sqr-sqrt` `add-exp-log`
12×	`add-cube-cbrt`
11×	`unpow-prod-down`
9×	`pow1`
6×	`pow-unpow` `sqrt-div`
5×	`sqrt-pow1` `pow-exp`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `times-frac` `pow1/2` `div-exp` `prod-exp` `distribute-lft-out`
2×	`pow-to-exp` `pow-pow` `flip3-+` `flip-+` `sqr-pow`
1×	`div-inv`

Counts

4 → 84

Calls

4 calls:

42.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
170.0ms	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
156.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
193.0ms	(pow (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0) 1/4)

series2.1s

Counts

4 → 12

Calls

4 calls:

399.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
666.0ms	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
341.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
689.0ms	(pow (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0) 1/4)

simplify5.2s

Counts

96 → 96

Iterations

Iter	Nodes
done	5003
3	3565
2	1180
1	472
0	200

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 8.5b

localize263.0ms

Local error

Found 4 expressions with local error:

8.9b	(pow (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) 1/4)
8.9b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
8.9b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
8.9b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite624.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`sqrt-prod`
13×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`pow1`
7×	`unpow-prod-down`
6×	`sqrt-div`
5×	`add-exp-log`
4×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `insert-posit16` `distribute-lft-out` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `pow-pow` `flip3-+` `flip-+`
1×	`pow-to-exp` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

128.0ms	(pow (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) 1/4)
164.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
149.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
178.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series1.9s

Counts

4 → 12

Calls

4 calls:

840.0ms	(pow (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) 1/4)
313.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
361.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
354.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify3.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
3	1718
2	644
1	250
0	103

prune1.2s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 8.5b

regimes1.5s

Accuracy

12.3% (8.1b remaining)

Error of 16.8b against oracle of 8.7b and baseline of 17.9b

bsearch329.0ms

Steps

Iters	Range		Point
8	3.0862339173164288e+128	2.4645549843776196e+131	3.6995689240091287e+130
9	-1.971781211500644e+165	-1.6602605836509326e+158	-2.046031859409107e+163

simplify25.0ms

Iterations

Iter	Nodes
done	36
1	36
0	26

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.1s	1519×	body	1280	valid
1.1s	1262×	body	640	valid
907.0ms	4242×	body	80	valid
324.0ms	647×	body	320	valid
75.0ms	332×	body	160	valid