Details

sample65.0ms

Algorithm

intervals

Results

22.0ms	43×	body	1280	valid
14.0ms	46×	body	640	valid
9.0ms	134×	body	80	valid
6.0ms	26×	body	320	valid
1.0ms	7×	body	160	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	13
1	75	13
2	139	13
3	207	13
4	375	13
5	1364	13
6	5002	13

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 18.9b

Counts

2 → 1

localize15.0ms

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)
6.9b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.7b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-l`
5×	`*-commutative`
4×	`sqrt-div`
2×	`flip3-+` `associate-*r/` `flip-+`
1×	`pow-to-exp` `unpow-prod-down` `pow1/2` `div-inv` `sqr-pow`

Counts

4 → 16

Calls

4 calls:

4.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
3.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
4.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
127.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
184.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
148.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	202	238
1	520	236
2	1556	236
3	5002	232

prune111.0ms

Filtered

28 candidates to 25 candidates (89.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	24	4	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	24	5	29

Merged error: 12.7b

Counts

29 → 5

localize15.0ms

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)
7.2b	(* J (* (* -2.0 (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
10.7b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-commutative`
4×	`sqrt-div` `associate-r/` `associate-r` `associate-l*`
2×	`flip3-+` `flip-+`
1×	`pow-to-exp` `unpow-prod-down` `pow1/2` `div-inv` `sqr-pow`

Counts

4 → 16

Calls

4 calls:

4.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
3.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.0ms	(* J (* (* -2.0 (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
4.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
130.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
186.0ms	(* J (* (* -2.0 (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
144.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	200	210
1	505	208
2	1544	208
3	5001	204

prune107.0ms

Filtered

28 candidates to 25 candidates (89.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	28	5	33

Merged error: 12.7b

Counts

33 → 5

localize31.0ms

Local error

Found 4 expressions with local error:

2.6b	(* (* (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) -2.0) (* J (cos (/ K 2.0))))
5.6b	(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
15.0b	(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
21.3b	(/ (* (* (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) -2.0) (* J (cos (/ K 2.0)))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

41×	`sqr-pow`
36×	`associate-r` `prod-diff`
32×	`div-inv`
31×	`unpow-prod-down`
24×	`*-commutative`
14×	`associate-l`
10×	`swap-sqr`
9×	`fma-neg`
6×	`associate-/l*`
5×	`unswap-sqr`
4×	`distribute-rgt-out--` `sqrt-div`
2×	`flip3-+` `associate-/r/` `flip-+` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `frac-2neg` `pow1/2` `clear-num` `flip--`

Counts

4 → 74

Calls

4 calls:

6.0ms	(* (* (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) -2.0) (* J (cos (/ K 2.0))))
21.0ms	(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
21.0ms	(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
22.0ms	(/ (* (* (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) -2.0) (* J (cos (/ K 2.0)))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))

series3.1s

Counts

4 → 12

Calls

4 calls:

654.0ms	(* (* (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) -2.0) (* J (cos (/ K 2.0))))
490.0ms	(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
478.0ms	(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
1.5s	(/ (* (* (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) -2.0) (* J (cos (/ K 2.0)))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))

simplify91.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	784	2890
1	3056	2180
2	5001	2166

prune380.0ms

Filtered

86 candidates to 50 candidates (58.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	84	7	91

Merged error: 12.7b

Counts

91 → 7

localize32.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) J)
5.6b	(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
15.0b	(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
23.2b	(/ (* (* (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) -2.0) (cos (/ K 2.0))) (/ (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) J))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

41×	`sqr-pow`
38×	`div-inv`
36×	`prod-diff`
32×	`associate-r`
31×	`unpow-prod-down`
22×	`*-commutative`
14×	`associate-l`
10×	`swap-sqr`
9×	`fma-neg`
6×	`sqrt-div`
5×	`associate-/r/` `unswap-sqr`
4×	`distribute-rgt-out--` `times-frac` `associate-/l/` `associate-/l*`
3×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `pow1/2` `associate-/r*` `flip--`

Counts

4 → 80

Calls

4 calls:

19.0ms	(/ (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) J)
26.0ms	(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
18.0ms	(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
23.0ms	(/ (* (* (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) -2.0) (cos (/ K 2.0))) (/ (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) J))

series3.1s

Counts

4 → 12

Calls

4 calls:

390.0ms	(/ (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) J)
499.0ms	(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
508.0ms	(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
1.7s	(/ (* (* (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) -2.0) (cos (/ K 2.0))) (/ (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) J))

simplify95.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	801	3185
1	3104	2471
2	5002	2449

prune520.0ms

Filtered

92 candidates to 54 candidates (58.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	93	6	99

Merged error: 12.7b

Counts

99 → 6

regimes242.0ms

Accuracy

90.3% (0.5b remaining)

Error of 13.3b against oracle of 12.7b and baseline of 18.2b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	50
1	45	50

end0.0ms

sample1.8s

Algorithm

intervals

Results

695.0ms	1514×	body	1280	valid
405.0ms	1261×	body	640	valid
318.0ms	4278×	body	80	valid
151.0ms	640×	body	320	valid
48.0ms	310×	body	160	valid