Details

sample132.0ms

Algorithm

intervals

Results

65.0ms	146×	body	1280	valid
30.0ms	122×	body	640	valid
10.0ms	58×	body	320	valid
7.0ms	151×	body	80	valid
4.0ms	43×	body	160	valid

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	40	7
2	92	7
3	163	7
4	405	7
5	865	7
6	1189	7
7	2769	7
8	5001	7

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: 45.0b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))
5.1b	(- (exp (- im)) (exp im))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

3×	`sub-neg`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-r/` `associate-l` `-commutative` `flip--`

Counts

2 → 13

Calls

2 calls:

6.0ms	(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))
3.0ms	(- (exp (- im)) (exp im))

series122.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(* (* 0.5 (sin re)) (- (exp (- im)) (exp im)))
37.0ms	(- (exp (- im)) (exp im))

simplify46.0ms

Algorithm

egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	135	138
1	385	132
2	1204	126
3	5001	121

prune57.0ms

Filtered

19 candidates to 12 candidates (63.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	16	3	19
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	17	3	20

Merged error: 0.1b

Counts

20 → 3

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/60 (pow im 5))
0.1b	(* (* 0.5 (sin re)) (fma im -2 (- (fma (pow im 3) 1/3 (* 1/60 (pow im 5))))))
0.1b	(fma (pow im 3) 1/3 (* 1/60 (pow im 5)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-commutative` `fma-udef`
2×	`associate-l`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `sqr-pow`

Counts

3 → 8

Calls

3 calls:

3.0ms	(* 1/60 (pow im 5))
4.0ms	(* (* 0.5 (sin re)) (fma im -2 (- (fma (pow im 3) 1/3 (* 1/60 (pow im 5))))))
1.0ms	(fma (pow im 3) 1/3 (* 1/60 (pow im 5)))

series358.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* 1/60 (pow im 5))
179.0ms	(* (* 0.5 (sin re)) (fma im -2 (- (fma (pow im 3) 1/3 (* 1/60 (pow im 5))))))
125.0ms	(fma (pow im 3) 1/3 (* 1/60 (pow im 5)))

simplify140.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	105	91
1	291	89
2	942	89
3	3945	81
4	5001	81

prune44.0ms

Filtered

17 candidates to 10 candidates (58.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	17	0	17
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	17	3	20

Merged error: 0.1b

Counts

20 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp im) -2)
0.0b	(pow (exp im) 3)
0.1b	(pow (exp (- im)) 3)
4.9b	(- (pow (exp (- im)) 3) (pow (exp im) 3))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`sqr-pow`
7×	`unpow3`
4×	`prod-diff`
3×	`pow-to-exp` `pow-exp`
2×	`fma-neg`
1×	`difference-cubes` `neg-mul-1` `sub-neg` `exp-prod` `flip3--` `pow-pow` `flip--` `difference-of-squares`

Counts

4 → 24

Calls

4 calls:

2.0ms	(pow (exp im) -2)
2.0ms	(pow (exp im) 3)
2.0ms	(pow (exp (- im)) 3)
6.0ms	(- (pow (exp (- im)) 3) (pow (exp im) 3))

series167.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (exp im) -2)
24.0ms	(pow (exp im) 3)
27.0ms	(pow (exp (- im)) 3)
94.0ms	(- (pow (exp (- im)) 3) (pow (exp im) 3))

simplify176.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 3 (172.0ms)

Iter	Nodes	Cost
0	213	222
1	732	187
2	3633	180
3	5001	175

prune121.0ms

Filtered

36 candidates to 22 candidates (61.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	34	2	36
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	36	3	39

Merged error: 0.1b

Counts

39 → 3

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp im) -2)
0.1b	(* 9 (pow im 3))
0.1b	(* (* 0.5 (sin re)) (/ (- (- (* 9 (pow im 3))) (fma 81/20 (pow im 5) (* 6 im))) (fma (pow (exp im) -2) 1 (fma (exp im) (exp im) 1))))
0.2b	(/ (- (- (* 9 (pow im 3))) (fma 81/20 (pow im 5) (* 6 im))) (fma (pow (exp im) -2) 1 (fma (exp im) (exp im) 1)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

5×	`associate-*r/`
4×	`associate-/l/`
3×	`div-sub` `associate-r` `clear-num` `*-commutative`
2×	`flip3--` `frac-2neg` `associate-l` `flip--` `div-inv` `sqr-pow`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `unpow3` `pow-exp` `un-div-inv` `fma-udef` `associate--r+`

Counts

4 → 24

Calls

4 calls:

2.0ms	(pow (exp im) -2)
3.0ms	(* 9 (pow im 3))
8.0ms	(* (* 0.5 (sin re)) (/ (- (- (* 9 (pow im 3))) (fma 81/20 (pow im 5) (* 6 im))) (fma (pow (exp im) -2) 1 (fma (exp im) (exp im) 1))))
6.0ms	(/ (- (- (* 9 (pow im 3))) (fma 81/20 (pow im 5) (* 6 im))) (fma (pow (exp im) -2) 1 (fma (exp im) (exp im) 1)))

series577.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (exp im) -2)
40.0ms	(* 9 (pow im 3))
313.0ms	(* (* 0.5 (sin re)) (/ (- (- (* 9 (pow im 3))) (fma 81/20 (pow im 5) (* 6 im))) (fma (pow (exp im) -2) 1 (fma (exp im) (exp im) 1))))
205.0ms	(/ (- (- (* 9 (pow im 3))) (fma 81/20 (pow im 5) (* 6 im))) (fma (pow (exp im) -2) 1 (fma (exp im) (exp im) 1)))

simplify39.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	323	405
1	1170	393
2	5001	350

prune149.0ms

Filtered

36 candidates to 26 candidates (72.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	31	5	36
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	32	7	39

Merged error: 0.1b

Counts

39 → 7

regimes193.0ms

Accuracy

0% (0.6b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.1s	4753×	body	1280	valid
958.0ms	3822×	body	640	valid
285.0ms	1790×	body	320	valid
229.0ms	4667×	body	80	valid
105.0ms	997×	body	160	valid