Details

sample101.0ms

Algorithm

intervals

Results

36.0ms	84×	body	1280	valid
22.0ms	87×	body	640	valid
14.0ms	257×	body	80	valid
7.0ms	40×	body	320	valid
3.0ms	26×	body	160	valid

simplify367.0ms

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	4980	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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 18.2b

Counts

2 → 1

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
7.6b	(- (exp l) (exp (- l)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`prod-diff`
24×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
5×	`pow1` `add-exp-log` `associate-r` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `sub-neg` `fma-neg` `associate-l` `log1p-expm1-u`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 84

Calls

3 calls:

8.0ms	(* J (- (exp l) (exp (- l))))
1.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
6.0ms	(- (exp l) (exp (- l)))

series261.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* J (- (exp l) (exp (- l))))
168.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
35.0ms	(- (exp l) (exp (- l)))

simplify41.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	318	1176
1	1096	780
2	5001	725

prune224.0ms

Filtered

93 candidates to 56 candidates (60.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	2	94

Merged error: 0.0b

Counts

94 → 2

localize17.0ms

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

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)))
3.0ms	(* J (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)

series683.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(fma 1/60 (pow l 5) (* 2 l))
56.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
132.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
374.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify110.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	186	510
1	795	442
2	4250	434
3	5001	434

prune229.0ms

Filtered

64 candidates to 49 candidates (76.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	60	6	66

Merged error: 0.0b

Counts

66 → 6

localize20.0ms

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	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.2b	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`

Counts

4 → 62

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)))
3.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
5.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(fma 1/60 (pow l 5) (* 2 l))
56.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
131.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
166.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	229	634
1	1154	529
2	5001	521

prune229.0ms

Filtered

74 candidates to 52 candidates (70.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	74	6	80

Merged error: 0.0b

Counts

80 → 6

localize20.0ms

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

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)))
4.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))
5.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))

series426.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(fma 1/60 (pow l 5) (* 2 l))
56.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
86.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))
162.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))

simplify39.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	229	677
1	955	567
2	5001	566

prune208.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	6	78

Merged error: 0.0b

Counts

78 → 6

regimes219.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.2s	2754×	body	1280	valid
704.0ms	2604×	body	640	valid
488.0ms	8598×	body	80	valid
249.0ms	1397×	body	320	valid
90.0ms	770×	body	160	valid