Details

sample137.0ms

Algorithm

intervals

Results

42.0ms	46×	body	1280	valid
28.0ms	42×	body	640	valid
22.0ms	132×	body	80	valid
10.0ms	21×	body	320	valid
5.0ms	15×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	34	24
2	72	24
3	133	24
4	194	24
5	315	24
6	754	24
7	2539	24
done	5001	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite447.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-cbrt-cube`
18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`pow1`
12×	`add-cube-cbrt` `prod-exp`
9×	`cbrt-unprod`
8×	`unpow-prod-down` `sqrt-prod`
7×	`associate-r`
6×	`times-frac` `div-exp` `pow-prod-down`
4×	`expm1-log1p-u` `sqrt-div` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `hypot-def` `associate-/l*`
2×	`flip3-+` `associate-*r/` `flip-+` `div-inv` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l` `clear-num` `associate-/r` `-commutative`

Counts

4 → 101

Calls

4 calls:

24.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
32.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
248.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
137.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series903.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
197.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
298.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
249.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.4s

Counts

113 → 113

Iterations

Useful iterations: 2 (497.0ms)

Iter	Nodes	Cost
0	222	2298
1	543	2082
2	1970	1861
done	5000	1861

prune658.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
6.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite180.0ms

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:

21.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
30.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
38.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
89.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series1.0s

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
74.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
134.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
765.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify1.6s

Counts

100 → 100

Iterations

Useful iterations: 2 (435.0ms)

Iter	Nodes	Cost
0	193	1843
1	478	1816
2	1912	1415
done	5001	1415

prune574.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))) (cos (/ K 2.0)))
0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
6.5b	(* (* -2.0 J) (* (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))) (cos (/ K 2.0))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

9.0ms	(* (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))) (cos (/ K 2.0)))
20.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
20.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
65.0ms	(* (* -2.0 J) (* (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))) (cos (/ K 2.0))))

series1.7s

Counts

4 → 12

Calls

4 calls:

739.0ms	(* (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))) (cos (/ K 2.0)))
83.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
118.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
741.0ms	(* (* -2.0 J) (* (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))) (cos (/ K 2.0))))

simplify1.7s

Counts

101 → 101

Iterations

Useful iterations: 2 (520.0ms)

Iter	Nodes	Cost
0	194	2329
1	476	2302
2	1844	1792
done	5001	1792

prune606.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
0.1b	(* (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))) (cos (/ K 2.0)))
0.2b	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
6.5b	(* (* -2.0 J) (* (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))) (cos (/ K 2.0))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
27×	`add-exp-log` `add-cbrt-cube`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
10×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down`
7×	`associate-/l*`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`*-commutative`
1×	`hypot-udef` `frac-2neg` `clear-num` `associate-/l/` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

1.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
18.0ms	(* (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))) (cos (/ K 2.0)))
46.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
41.0ms	(* (* -2.0 J) (* (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))) (cos (/ K 2.0))))

series2.4s

Counts

4 → 12

Calls

4 calls:

686.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
748.0ms	(* (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))) (cos (/ K 2.0)))
162.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
825.0ms	(* (* -2.0 J) (* (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))) (cos (/ K 2.0))))

simplify1.8s

Counts

116 → 116

Iterations

Useful iterations: 2 (388.0ms)

Iter	Nodes	Cost
0	239	2897
1	557	2813
2	1801	2343
done	5001	2343

prune723.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

regimes393.0ms

Accuracy

0% (0.3b remaining)

Error of 7.9b against oracle of 7.6b and baseline of 7.9b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	26
1	23	26
done	23	26

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.5s	1528×	body	1280	valid
1.2s	4294×	body	80	valid
996.0ms	1234×	body	640	valid
252.0ms	610×	body	320	valid
96.0ms	335×	body	160	valid