Details

sample135.0ms

Algorithm

intervals

Results

79.0ms	191×	body	1280	valid
24.0ms	104×	body	640	valid
7.0ms	48×	body	320	valid
7.0ms	161×	body	80	valid
2.0ms	21×	body	160	valid

simplify89.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	44	7
2	104	7
3	213	7
4	364	7
5	850	7
6	1415	7
7	1968	7
8	4985	7
9	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: 58.4b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
6.5b	(- (exp (- 0.0 im)) (exp im))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

216×	`prod-diff`
119×	`add-sqr-sqrt` `*-un-lft-identity`
115×	`add-cube-cbrt`
110×	`exp-sum`
44×	`distribute-rgt-in` `distribute-lft-in`
14×	`fma-neg`
13×	`sub-neg`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-r`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `associate-l` `*-commutative`

Counts

2 → 184

Calls

2 calls:

18.0ms	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
12.0ms	(- (exp (- 0.0 im)) (exp im))

series114.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
35.0ms	(- (exp (- 0.0 im)) (exp im))

simplify82.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	714	4198
1	2514	2591
2	5003	2251

prune230.0ms

Filtered

190 candidates to 53 candidates (27.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	188	3	191

Merged error: 0.1b

Counts

191 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/60 (pow im 5) (* 2 im))
0.0b	(- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))
0.1b	(* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
0.1b	(* 1/3 (pow im 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

54×	`prod-diff`
48×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
37×	`add-cube-cbrt`
20×	`distribute-rgt-in` `distribute-lft-in`
17×	`associate-r`
14×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
9×	`pow1`
8×	`add-log-exp`
6×	`fma-neg` `prod-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `associate-l` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `pow-prod-down`
2×	`flip3--` `diff-log` `associate-r/` `-commutative` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`associate--l-` `neg-sub0` `cube-mult` `pow-to-exp` `unpow3` `neg-log` `pow-exp` `associate--r+`

Counts

4 → 150

Calls

4 calls:

1.0ms	(fma 1/60 (pow im 5) (* 2 im))
6.0ms	(- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))
11.0ms	(* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
6.0ms	(* 1/3 (pow im 3))

series394.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(fma 1/60 (pow im 5) (* 2 im))
58.0ms	(- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))
170.0ms	(* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))
39.0ms	(* 1/3 (pow im 3))

simplify91.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	603	2649
1	2648	1687
2	5001	1676

prune373.0ms

Filtered

162 candidates to 79 candidates (48.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	155	7	162
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	156	9	165

Merged error: 0.0b

Counts

165 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (* (cos re) (* -1/3 (pow im 3))))
0.1b	(* (cos re) (* -1/3 (pow im 3)))
0.1b	(* (* 0.5 (cos re)) (- (fma 1/60 (pow im 5) (* 2 im))))
0.1b	(* -1/3 (pow im 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log`
25×	`prod-exp` `add-cbrt-cube`
24×	`associate-r`
20×	`add-sqr-sqrt`
16×	`pow1`
13×	`add-cube-cbrt` `*-un-lft-identity` `cbrt-unprod`
10×	`associate-l`
7×	`pow-prod-down`
4×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `*-commutative` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-lft-neg-in` `pow-to-exp` `distribute-rgt-neg-in` `pow-exp`
2×	`distribute-neg-in` `fma-udef` `sqr-pow`
1×	`distribute-rgt-in` `cube-mult` `neg-mul-1` `distribute-lft-in` `unpow3` `distribute-rgt-neg-out`

Counts

4 → 108

Calls

4 calls:

8.0ms	(* 0.5 (* (cos re) (* -1/3 (pow im 3))))
6.0ms	(* (cos re) (* -1/3 (pow im 3)))
6.0ms	(* (* 0.5 (cos re)) (- (fma 1/60 (pow im 5) (* 2 im))))
6.0ms	(* -1/3 (pow im 3))

series503.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* 0.5 (* (cos re) (* -1/3 (pow im 3))))
95.0ms	(* (cos re) (* -1/3 (pow im 3)))
272.0ms	(* (* 0.5 (cos re)) (- (fma 1/60 (pow im 5) (* 2 im))))
40.0ms	(* -1/3 (pow im 3))

simplify77.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	498	740
1	2490	627
2	5001	627

prune382.0ms

Filtered

120 candidates to 76 candidates (63.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	120	9	129

Merged error: 0.0b

Counts

129 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))) (cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))))
0.7b	(cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))
0.7b	(cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))
0.7b	(cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*r/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3--` `pow1/3` `flip--`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

9.0ms	(* (cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))) (cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))))
7.0ms	(cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))
7.0ms	(cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))
7.0ms	(cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

552.0ms	(* (cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))) (cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im))))))
312.0ms	(cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))
312.0ms	(cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))
321.0ms	(cbrt (* (* 0.5 (cos re)) (- (- (* 1/3 (pow im 3))) (fma 1/60 (pow im 5) (* 2 im)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	434	2047
1	1697	1877
2	5002	1776

prune642.0ms

Filtered

92 candidates to 78 candidates (84.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	91	10	101

Merged error: 0.0b

Counts

101 → 10

regimes235.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	13
1	33	13
2	40	13
3	40	13

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.3s	5673×	body	1280	valid
853.0ms	3621×	body	640	valid
223.0ms	1470×	body	320	valid
194.0ms	4381×	body	80	valid
72.0ms	696×	body	160	valid