Details

sample144.0ms

Algorithm

intervals

Results

77.0ms	171×	body	1280	valid
34.0ms	116×	body	640	valid
7.0ms	42×	body	320	valid
7.0ms	131×	body	80	valid
2.0ms	21×	body	160	valid

simplify86.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	7
1	44	7
2	99	7
3	185	7
4	318	7
5	766	7
6	1270	7
7	1801	7
8	4743	7
9	5001	7

prune2.0ms

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: 56.3b

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)))
5.8b	(- (exp (- 0.0 im)) (exp im))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
5×	`associate-r`
4×	`add-log-exp`
3×	`add-cube-cbrt` `sub-neg` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `associate-l` `*-commutative`

Counts

2 → 40

Calls

2 calls:

12.0ms	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
7.0ms	(- (exp (- 0.0 im)) (exp im))

series120.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
40.0ms	(- (exp (- 0.0 im)) (exp im))

simplify38.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	268	399
1	1086	345
2	5001	344

prune112.0ms

Filtered

46 candidates to 30 candidates (65.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	5	47

Merged error: 0.1b

Counts

47 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

29×	`associate-r`
26×	`add-sqr-sqrt`
19×	`add-exp-log`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-cbrt-cube`
9×	`pow1` `prod-exp` `add-log-exp`
8×	`unpow-prod-down`
7×	`associate-l` `unswap-sqr`
5×	`cbrt-unprod`
4×	`cube-prod` `sqr-pow`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `pow-prod-down` `sum-log` `*-commutative`
2×	`pow-to-exp` `distribute-neg-in` `flip3-+` `associate-*r/` `pow-exp` `flip-+` `distribute-neg-frac`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `neg-mul-1` `associate-+r+` `distribute-lft-in` `unpow3` `distribute-rgt-neg-out`

Counts

4 → 99

Calls

4 calls:

8.0ms	(+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))
5.0ms	(* 1/60 (pow im 5))
12.0ms	(* (* 0.5 (cos re)) (- (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))))
6.0ms	(* 1/3 (pow im 3))

series324.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))
46.0ms	(* 1/60 (pow im 5))
176.0ms	(* (* 0.5 (cos re)) (- (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))))
41.0ms	(* 1/3 (pow im 3))

simplify82.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	541	829
1	2757	736
2	5001	733

prune302.0ms

Filtered

111 candidates to 70 candidates (63.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	105	11	116

Merged error: 0.0b

Counts

116 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

29×	`associate-r`
26×	`add-sqr-sqrt`
19×	`add-exp-log`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-cbrt-cube`
9×	`pow1` `prod-exp`
8×	`unpow-prod-down`
7×	`associate-l` `unswap-sqr`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`cube-prod` `sqr-pow`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `pow-prod-down` `*-commutative`
2×	`pow-to-exp` `distribute-neg-in` `flip3-+` `associate-*r/` `pow-exp` `flip-+` `distribute-neg-frac`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `neg-mul-1` `distribute-lft-in` `unpow3` `sum-log` `distribute-rgt-neg-out`

Counts

4 → 97

Calls

4 calls:

5.0ms	(+ (* 1/3 (pow im 3)) (* 1/60 (pow im 5)))
5.0ms	(* 1/60 (pow im 5))
7.0ms	(* 1/3 (pow im 3))
11.0ms	(* (* 0.5 (cos re)) (- (+ (+ (* 1/3 (pow im 3)) (* 1/60 (pow im 5))) (* 2 im))))

series593.0ms

Counts

4 → 12

Calls

4 calls:

328.0ms	(+ (* 1/3 (pow im 3)) (* 1/60 (pow im 5)))
46.0ms	(* 1/60 (pow im 5))
41.0ms	(* 1/3 (pow im 3))
178.0ms	(* (* 0.5 (cos re)) (- (+ (+ (* 1/3 (pow im 3)) (* 1/60 (pow im 5))) (* 2 im))))

simplify83.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	545	760
1	2666	683
2	5001	683

prune272.0ms

Filtered

109 candidates to 70 candidates (64.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	109	11	120

Merged error: 0.0b

Counts

120 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))) (cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))))
0.6b	(cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im))))
0.6b	(cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im))))
0.6b	(cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

17.0ms	(* (cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))) (cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))))
7.0ms	(cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im))))
7.0ms	(cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im))))
7.0ms	(cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im))))

series654.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))) (cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))))
161.0ms	(cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im))))
160.0ms	(cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im))))
154.0ms	(cbrt (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im))))

simplify62.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	393	2049
1	1443	1928
2	5001	1792

prune394.0ms

Filtered

99 candidates to 75 candidates (75.8%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	97	13	110

Merged error: 0.0b

Counts

110 → 13

regimes427.0ms

Accuracy

42.8% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	25
1	56	25
2	75	25
3	75	25

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.6s	5734×	body	1280	valid
971.0ms	3602×	body	640	valid
265.0ms	1496×	body	320	valid
238.0ms	4572×	body	80	valid
77.0ms	683×	body	160	valid