Details

sample65.0ms

Algorithm

intervals

Results

22.0ms	46×	body	1280	valid
13.0ms	42×	body	640	valid
9.0ms	133×	body	80	valid
5.0ms	21×	body	320	valid
2.0ms	14×	body	160	valid

simplify46.0ms

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	1373	13
6	5001	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: 19.4b

Counts

2 → 1

localize16.0ms

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)
8.6b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite35.0ms

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:

5.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
7.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
14.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
130.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
181.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
142.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	464	1076
1	1988	966
2	5001	965

prune329.0ms

Filtered

108 candidates to 73 candidates (67.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	100	8	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Merged error: 8.9b

Counts

109 → 8

localize17.0ms

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)))
8.6b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite28.0ms

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:

9.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
5.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
5.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
7.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series667.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
43.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
49.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
490.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify59.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	489	993
1	2344	770
2	5001	770

prune311.0ms

Filtered

100 candidates to 66 candidates (66.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	93	7	100
Fresh	6	1	7
Picked	0	1	1
Done	0	0	0
Total	99	9	108

Merged error: 8.8b

Counts

108 → 9

localize17.0ms

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)))
8.6b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

rewrite22.0ms

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:

1.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
5.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
7.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
7.0ms	(* (* (* -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:

408.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
44.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
86.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
484.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

simplify66.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	575	1308
1	2599	1083
2	5001	1083

prune425.0ms

Filtered

115 candidates to 86 candidates (74.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	115	9	124

Merged error: 8.8b

Counts

124 → 9

localize16.0ms

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	(* (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)))
8.6b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

rewrite24.0ms

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)))
3.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
6.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
6.0ms	(* (* -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:

479.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
422.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
86.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
598.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	605	1555
1	2672	1277
2	5002	1276

prune385.0ms

Filtered

116 candidates to 87 candidates (75.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	116	9	125

Merged error: 8.8b

Counts

125 → 9

regimes227.0ms

Accuracy

0% (0.3b remaining)

Error of 7.8b against oracle of 7.5b and baseline of 7.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	14
1	24	14

end0.0ms

sample1.7s

Algorithm

intervals

Results

631.0ms	1426×	body	1280	valid
371.0ms	1218×	body	640	valid
316.0ms	4440×	body	80	valid
127.0ms	586×	body	320	valid
52.0ms	332×	body	160	valid