Details

sample133.0ms

Algorithm

intervals

Results

56.0ms	52×	body	1280	valid
22.0ms	46×	body	640	valid
19.0ms	127×	body	80	valid
7.0ms	20×	body	320	valid
2.0ms	11×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	34	24
2	72	24
3	136	24
4	214	24
5	498	24
6	3356	24
done	5002	24

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.7b

localize21.0ms

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)
7.9b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
20×	`pow1`
18×	`add-cbrt-cube`
17×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`prod-exp`
11×	`add-cube-cbrt`
10×	`associate-r`
9×	`pow-prod-down` `cbrt-unprod`
8×	`unpow-prod-down` `sqrt-prod`
4×	`expm1-log1p-u` `sqrt-div` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp` `hypot-def`
2×	`flip3-+` `associate-r/` `associate-l` `-commutative` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 96

Calls

4 calls:

22.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
31.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
206.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
89.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series733.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
177.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
283.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
207.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.8s

Counts

108 → 108

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	201	2139
1	519	1925
2	2469	1748
done	5001	1736

prune528.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
7.9b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
23×	`pow1`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
9×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-l` `-commutative` `associate-/l`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 88

Calls

4 calls:

30.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
28.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
23.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
83.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series912.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
60.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
57.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
687.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify1.7s

Counts

100 → 100

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	193	1843
1	497	1816
2	3042	1449
done	5000	1447

prune564.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.1b

localize69.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (* (* -2.0 J) (cos (/ K 2.0))) (* (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
8.1b	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
8.1b	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
8.1b	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1` `add-exp-log`
19×	`add-cbrt-cube`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`associate-r` `associate-l` `*-commutative`

Counts

4 → 69

Calls

4 calls:

145.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (* (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
2.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
2.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
2.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series3.3s

Counts

4 → 12

Calls

4 calls:

910.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (* (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
789.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
755.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
813.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify915.0ms

Counts

81 → 81

Iterations

Useful iterations: done (911.0ms)

Iter	Nodes	Cost
0	135	3184
1	341	3034
2	1320	2441
done	5000	2333

prune618.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 8.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (* -2.0 J) (cos (/ K 2.0))))
0.6b	(cbrt (* (* -2.0 J) (cos (/ K 2.0))))
0.6b	(cbrt (* (* -2.0 J) (cos (/ K 2.0))))
7.9b	(* (* (* (cbrt (* (* -2.0 J) (cos (/ K 2.0)))) (cbrt (* (* -2.0 J) (cos (/ K 2.0))))) (cbrt (* (* -2.0 J) (cos (/ K 2.0))))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite378.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log`
9×	`add-cbrt-cube`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `associate-r`
1×	`associate-l` `*-commutative`

Counts

4 → 56

Calls

4 calls:

25.0ms	(cbrt (* (* -2.0 J) (cos (/ K 2.0))))
28.0ms	(cbrt (* (* -2.0 J) (cos (/ K 2.0))))
26.0ms	(cbrt (* (* -2.0 J) (cos (/ K 2.0))))
296.0ms	(* (* (* (cbrt (* (* -2.0 J) (cos (/ K 2.0)))) (cbrt (* (* -2.0 J) (cos (/ K 2.0))))) (cbrt (* (* -2.0 J) (cos (/ K 2.0))))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series1.5s

Counts

4 → 12

Calls

4 calls:

208.0ms	(cbrt (* (* -2.0 J) (cos (/ K 2.0))))
264.0ms	(cbrt (* (* -2.0 J) (cos (/ K 2.0))))
235.0ms	(cbrt (* (* -2.0 J) (cos (/ K 2.0))))
811.0ms	(* (* (* (cbrt (* (* -2.0 J) (cos (/ K 2.0)))) (cbrt (* (* -2.0 J) (cos (/ K 2.0))))) (cbrt (* (* -2.0 J) (cos (/ K 2.0))))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify951.0ms

Counts

68 → 68

Iterations

Useful iterations: done (948.0ms)

Iter	Nodes	Cost
0	135	2022
1	319	1979
2	1374	1250
done	5000	1151

prune428.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 8.1b

regimes489.0ms

Accuracy

0% (0.3b remaining)

Error of 8.0b against oracle of 7.7b and baseline of 8.0b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	26
1	24	26
done	24	26

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.9s	1542×	body	1280	valid
1.3s	1218×	body	640	valid
821.0ms	4308×	body	80	valid
241.0ms	619×	body	320	valid
141.0ms	317×	body	160	valid