Details

sample150.0ms

Algorithm

intervals

Results

63.0ms	52×	body	1280	valid
25.0ms	145×	body	80	valid
20.0ms	32×	body	640	valid
8.0ms	17×	body	320	valid
3.0ms	10×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 17.2b

localize27.0ms

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)
5.5b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite367.0ms

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:

39.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
26.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
191.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
105.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series752.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
168.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
287.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
195.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.5s

Counts

113 → 113

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	222	2298
1	613	2082
2	2883	1877
done	5001	1875

prune618.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize33.0ms

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))))
5.5b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite182.0ms

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:

27.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
26.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
37.0ms	(/ 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))))

series978.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
66.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
118.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
730.0ms	(* (* (* -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: 2 (376.0ms)

Iter	Nodes	Cost
0	193	1843
1	498	1816
2	2978	1437
done	5001	1437

prune547.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.7b

localize21.0ms

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	(* (* -2.0 J) (cos (/ K 2.0)))
0.1b	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
5.5b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

0.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
28.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
30.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
90.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

series1.6s

Counts

4 → 12

Calls

4 calls:

595.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
67.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
141.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
816.0ms	(* (* (* -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

115 → 115

Iterations

Useful iterations: 2 (517.0ms)

Iter	Nodes	Cost
0	238	2411
1	587	2336
2	3160	1982
done	5002	1982

prune567.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))
0.2b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))
5.5b	(sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
5.5b	(sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

rewrite774.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1`
27×	`add-exp-log` `add-cbrt-cube`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt` `associate-r` `sqrt-prod`
10×	`add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 85

Calls

4 calls:

695.0ms	(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))
70.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))
3.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
3.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

series2.7s

Counts

4 → 12

Calls

4 calls:

635.0ms	(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))
684.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))
676.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
683.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

simplify1.7s

Counts

97 → 97

Iterations

Useful iterations: 2 (366.0ms)

Iter	Nodes	Cost
0	156	3825
1	407	3009
2	2145	2451
done	5001	2451

prune564.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

regimes390.0ms

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

sample4.1s

Algorithm

intervals

Results

1.7s	1472×	body	1280	valid
870.0ms	1278×	body	640	valid
858.0ms	4308×	body	80	valid
226.0ms	628×	body	320	valid
81.0ms	314×	body	160	valid