Details

sample96.0ms

Algorithm

intervals

Results

31.0ms	72×	body	1280	valid
18.0ms	287×	body	80	valid
18.0ms	72×	body	640	valid
7.0ms	44×	body	320	valid
2.0ms	20×	body	160	valid

simplify374.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	8
1	44	8
2	91	8
3	195	8
4	332	8
5	652	8
6	1279	8
7	1694	8
8	4978	8
9	5001	8

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 16.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.1b	(- (exp l) (exp (- l)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
40×	`associate-l`
34×	`add-cube-cbrt`
27×	`prod-diff`
24×	`fma-def`
21×	`associate-r`
11×	`pow1` `add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
9×	`unswap-sqr`
8×	`add-log-exp`
5×	`*-commutative`
4×	`expm1-log1p-u` `associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `fma-neg` `flip--` `distribute-lft-out`
2×	`associate-*l/`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 151

Calls

4 calls:

24.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
8.0ms	(* J (- (exp l) (exp (- l))))
13.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.0ms	(- (exp l) (exp (- l)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
56.0ms	(* J (- (exp l) (exp (- l))))
92.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
36.0ms	(- (exp l) (exp (- l)))

simplify64.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	468	1677
1	1763	1244
2	5001	1207

prune332.0ms

Filtered

163 candidates to 106 candidates (65.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	3	164

Merged error: 0.0b

Counts

164 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0b	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.0b	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
0.1b	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

36×	`associate-l`
31×	`add-sqr-sqrt`
22×	`fma-def`
21×	`*-un-lft-identity`
15×	`add-cube-cbrt` `associate-r`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`unswap-sqr`
6×	`add-log-exp`
5×	`*-commutative`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-udef` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `flip-+`

Counts

4 → 103

Calls

4 calls:

1.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
4.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
15.0ms	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
9.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

series607.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
138.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
244.0ms	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
167.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	308	969
1	1381	867
2	5003	867

prune355.0ms

Filtered

115 candidates to 87 candidates (75.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	110	5	115
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	112	6	118

Merged error: 0b

Counts

118 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/60 (pow l 5) (* 2 l))
0.0b	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0b	(fma (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (* J (cos (/ K 2.0))) U)
0.1b	(* J (cos (/ K 2.0)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `fma-udef`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 50

Calls

4 calls:

1.0ms	(fma 1/60 (pow l 5) (* 2 l))
1.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
1.0ms	(fma (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (* J (cos (/ K 2.0))) U)
5.0ms	(* J (cos (/ K 2.0)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(fma 1/60 (pow l 5) (* 2 l))
57.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
135.0ms	(fma (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (* J (cos (/ K 2.0))) U)
45.0ms	(* J (cos (/ K 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	168	409
1	600	357
2	2524	349
3	5001	349

prune208.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	62	6	68

Merged error: 0b

Counts

68 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/60 (pow l 5) (* 2 l))
0.0b	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0b	(fma J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))) U)
0.1b	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `fma-udef`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 50

Calls

4 calls:

1.0ms	(fma 1/60 (pow l 5) (* 2 l))
1.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
1.0ms	(fma J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))) U)
5.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

series521.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(fma 1/60 (pow l 5) (* 2 l))
58.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
234.0ms	(fma J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))) U)
104.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

simplify115.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	191	556
1	716	483
2	4894	468
3	5001	468

prune188.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	62	6	68

Merged error: 0b

Counts

68 → 6

regimes220.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	2642×	body	1280	valid
667.0ms	2615×	body	640	valid
473.0ms	8571×	body	80	valid
239.0ms	1432×	body	320	valid
86.0ms	765×	body	160	valid