Details

sample78.0ms

Algorithm

intervals

Results

21.0ms	46×	body	1280	valid
19.0ms	45×	body	640	valid
13.0ms	144×	body	80	valid
4.0ms	15×	body	320	valid
1.0ms	6×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3236
5	492
4	208
3	135
2	71
1	34
0	17

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize67.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.5b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.9b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

27.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
18.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
163.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
84.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series772.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
200.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
304.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
182.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	2368
1	508
0	192

prune763.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.6b	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
9.9b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
23×	`pow1`
21×	`add-cbrt-cube`
14×	`prod-exp`
11×	`*-un-lft-identity` `pow-prod-down` `cbrt-unprod`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
7×	`unpow-prod-down`
4×	`sqrt-div` `associate-r` `pow-exp` `associate-*r/` `sqrt-prod` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp`
2×	`flip3-+` `associate-l` `*-commutative` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 82

Calls

4 calls:

28.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
17.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
104.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
90.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series802.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
202.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
304.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
226.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.8s

Counts

94 → 94

Iterations

Iter	Nodes
done	5002
2	2427
1	544
0	199

prune708.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.9b

localize111.0ms

Local error

Found 4 expressions with local error:

10.5b	(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
16.8b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.8b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.8b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
13×	`*-un-lft-identity`
12×	`cbrt-prod` `pow1`
9×	`sqrt-pow1` `flip3-+` `pow1/3` `flip-+`
8×	`sqrt-div`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`frac-times` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`distribute-lft-out`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 69

Calls

4 calls:

92.0ms	(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
27.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
50.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
49.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

307.0ms	(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
374.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
331.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
315.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.2s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
3	1220
2	441
1	214
0	116

prune817.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 14.9b

localize137.0ms

Local error

Found 4 expressions with local error:

9.9b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.5b	(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
16.8b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.8b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-div`
13×	`pow1` `*-un-lft-identity`
10×	`sqrt-pow1` `sqrt-div`
9×	`flip3-+` `flip-+`
8×	`cbrt-prod` `add-sqr-sqrt` `pow1/3`
7×	`add-cube-cbrt`
5×	`sqrt-prod`
4×	`frac-times` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`distribute-lft-out`
2×	`rem-sqrt-square` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus`

Counts

4 → 71

Calls

4 calls:

68.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
72.0ms	(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
38.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
26.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

193.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
299.0ms	(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
313.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
323.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.6s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
3	1411
2	512
1	240
0	132

prune865.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 14.9b

regimes468.0ms

Accuracy

0% (5.5b remaining)

Error of 18.5b against oracle of 13.0b and baseline of 18.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	23
1	23
0	17

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.8s	1520×	body	1280	valid
725.0ms	1296×	body	640	valid
690.0ms	4242×	body	80	valid
372.0ms	623×	body	320	valid
82.0ms	324×	body	160	valid