Details

sample83.0ms

Algorithm

intervals

Results

27.0ms	51×	body	1280	valid
15.0ms	148×	body	80	valid
12.0ms	35×	body	640	valid
5.0ms	18×	body	320	valid
1.0ms	4×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	34	24
2	72	24
3	135	24
4	209	24
5	495	24
6	3226	24
done	5000	24

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize49.0ms

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)
6.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite300.0ms

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-l` `associate-r/` `-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:

28.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
20.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
135.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
111.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series738.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
197.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
271.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
213.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.4s

Counts

108 → 108

Iterations

Useful iterations: 2 (432.0ms)

Iter	Nodes	Cost
0	200	2139
1	519	1925
2	2432	1736
done	5000	1736

prune737.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.7b

localize30.0ms

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)))
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))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

14.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
15.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
14.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
59.0ms	(* (* (* -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:

146.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
91.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
84.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
717.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify1.5s

Counts

100 → 100

Iterations

Useful iterations: 2 (526.0ms)

Iter	Nodes	Cost
0	194	1843
1	499	1816
2	3021	1447
done	5000	1447

prune830.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.6b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
23×	`pow1`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
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×	`clear-num` `associate-/r*` `frac-2neg` `div-inv` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

6.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
19.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
25.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
42.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

645.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
125.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
71.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
1.1s	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

simplify1.3s

Counts

101 → 101

Iterations

Useful iterations: 2 (456.0ms)

Iter	Nodes	Cost
0	207	2273
1	536	2247
2	3024	1760
done	5001	1760

prune605.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.6b

localize51.0ms

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
27×	`add-cbrt-cube` `add-exp-log`
24×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
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` `clear-num` `frac-2neg` `unswap-sqr` `associate-/l/`

Counts

4 → 104

Calls

4 calls:

0.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
6.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
26.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
43.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

series2.2s

Counts

4 → 12

Calls

4 calls:

616.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
680.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
159.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
708.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

simplify1.4s

Counts

116 → 116

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	258	2841
1	639	2767
2	3108	2321
done	5000	2309

prune752.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.6b

regimes780.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.4s	1203×	body	640	valid
1.3s	1509×	body	1280	valid
816.0ms	4345×	body	80	valid
263.0ms	645×	body	320	valid
77.0ms	299×	body	160	valid