Details

sample140.0ms

Algorithm

intervals

Results

76.0ms	195×	body	1280	valid
29.0ms	129×	body	640	valid
8.0ms	56×	body	320	valid
5.0ms	130×	body	80	valid
5.0ms	22×	body	160	valid

simplify83.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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: 58.5b

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)))
5.5b	(- (exp (- 0.0 im)) (exp im))

rewrite24.0ms

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:

16.0ms	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
7.0ms	(- (exp (- 0.0 im)) (exp im))

series119.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
37.0ms	(- (exp (- 0.0 im)) (exp im))

simplify35.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (30.0ms)

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

prune112.0ms

Filtered

46 candidates to 30 candidates (65.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	2	47

Merged error: 0.1b

Counts

47 → 2

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 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))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

29×	`associate-r`
25×	`add-sqr-sqrt`
18×	`add-exp-log`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-cbrt-cube`
9×	`prod-exp`
8×	`pow1` `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` `*-commutative` `add-log-exp`
2×	`pow-to-exp` `distribute-neg-in` `associate-*r/` `pow-exp` `distribute-neg-frac`
1×	`distribute-rgt-in` `cube-mult` `neg-mul-1` `distribute-lft-in` `flip3-+` `unpow3` `distribute-rgt-neg-out` `flip-+`

Counts

3 → 86

Calls

3 calls:

5.0ms	(* 1/60 (pow im 5))
11.0ms	(* (* 0.5 (cos re)) (- (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))))
6.0ms	(* 1/3 (pow im 3))

series272.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* 1/60 (pow im 5))
182.0ms	(* (* 0.5 (cos re)) (- (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))))
42.0ms	(* 1/3 (pow im 3))

simplify79.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	489	670
1	2435	589
2	5002	586

prune237.0ms

Filtered

95 candidates to 60 candidates (63.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	90	5	95
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	90	7	97

Merged error: 0.0b

Counts

97 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow im 6) 1/9)
0.1b	(* (- (* 0.5 (cos re))) (+ (- (* (+ (* 1/60 (pow im 5)) (* 2 im)) (+ (* 1/60 (pow im 5)) (* 2 im)))) (* (pow im 6) 1/9)))
0.1b	(* 1/3 (pow im 3))
28.9b	(/ (* (- (* 0.5 (cos re))) (+ (- (* (+ (* 1/60 (pow im 5)) (* 2 im)) (+ (* 1/60 (pow im 5)) (* 2 im)))) (* (pow im 6) 1/9))) (- (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
21×	`add-exp-log`
18×	`associate-r`
16×	`associate-l`
15×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
6×	`pow1`
4×	`cube-prod` `associate-*r/` `cbrt-unprod` `add-log-exp` `sqr-pow`
3×	`times-frac` `associate-/r` `-commutative`
2×	`cbrt-undiv` `distribute-lft-neg-out` `pow-to-exp` `flip3-+` `div-exp` `pow-exp` `associate-/r/` `flip-+` `associate-/l/`
1×	`distribute-lft-neg-in` `distribute-rgt-in` `cube-mult` `neg-mul-1` `flip3--` `distribute-rgt-neg-in` `frac-2neg` `distribute-lft-in` `unpow3` `distribute-frac-neg` `pow-prod-down` `clear-num` `flip--` `div-inv` `associate-/l*`

Counts

4 → 108

Calls

4 calls:

5.0ms	(* (pow im 6) 1/9)
10.0ms	(* (- (* 0.5 (cos re))) (+ (- (* (+ (* 1/60 (pow im 5)) (* 2 im)) (+ (* 1/60 (pow im 5)) (* 2 im)))) (* (pow im 6) 1/9)))
6.0ms	(* 1/3 (pow im 3))
21.0ms	(/ (* (- (* 0.5 (cos re))) (+ (- (* (+ (* 1/60 (pow im 5)) (* 2 im)) (+ (* 1/60 (pow im 5)) (* 2 im)))) (* (pow im 6) 1/9))) (- (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im))))

series1.0s

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (pow im 6) 1/9)
570.0ms	(* (- (* 0.5 (cos re))) (+ (- (* (+ (* 1/60 (pow im 5)) (* 2 im)) (+ (* 1/60 (pow im 5)) (* 2 im)))) (* (pow im 6) 1/9)))
35.0ms	(* 1/3 (pow im 3))
362.0ms	(/ (* (- (* 0.5 (cos re))) (+ (- (* (+ (* 1/60 (pow im 5)) (* 2 im)) (+ (* 1/60 (pow im 5)) (* 2 im)))) (* (pow im 6) 1/9))) (- (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im))))

simplify145.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	659	1702
1	4260	1430
2	5002	1430

prune415.0ms

Filtered

120 candidates to 83 candidates (69.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	119	8	127

Merged error: 0.0b

Counts

127 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

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))
0.1b	(* 1/3 (pow im 3))
0.2b	(* (sqrt (* (* 0.5 (cos re)) (- (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))))) (sqrt (* (* 0.5 (cos re)) (- (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

136×	`pow1`
74×	`pow-prod-down`
60×	`sqrt-pow1`
38×	`associate-r`
35×	`add-sqr-sqrt`
21×	`add-exp-log`
19×	`add-cube-cbrt` `*-un-lft-identity`
17×	`pow-prod-up`
16×	`associate-*r/`
15×	`add-cbrt-cube`
14×	`distribute-neg-frac`
12×	`pow1/2` `sqrt-div`
11×	`associate-l` `pow-sqr`
10×	`prod-exp`
9×	`unswap-sqr`
8×	`unpow-prod-down` `cube-prod`
7×	`flip3-+` `flip-+`
6×	`cbrt-unprod`
4×	`frac-times` `swap-sqr` `sqrt-prod` `*-commutative` `add-log-exp` `sqr-pow`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`cube-mult` `pow-to-exp` `distribute-neg-in` `unpow3` `associate-*l/` `pow-exp`
1×	`pow2` `distribute-rgt-in` `neg-mul-1` `distribute-lft-in` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `distribute-rgt-neg-out`

Counts

4 → 166

Calls

4 calls:

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))
6.0ms	(* 1/3 (pow im 3))
24.0ms	(* (sqrt (* (* 0.5 (cos re)) (- (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))))) (sqrt (* (* 0.5 (cos re)) (- (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))))))

series454.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (* 0.5 (cos re)) (- (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))))
42.0ms	(* 1/3 (pow im 3))
36.0ms	(* 1/3 (pow im 3))
194.0ms	(* (sqrt (* (* 0.5 (cos re)) (- (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))))) (sqrt (* (* 0.5 (cos re)) (- (+ (* 1/3 (pow im 3)) (+ (* 1/60 (pow im 5)) (* 2 im)))))))

simplify127.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	642	1774
1	3453	1577
2	5002	1474

prune422.0ms

Filtered

178 candidates to 87 candidates (48.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	178	8	186

Merged error: 0.0b

Counts

186 → 8

regimes215.0ms

Accuracy

0% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	11
1	46	11
2	65	11
3	65	11

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.3s	5759×	body	1280	valid
823.0ms	3538×	body	640	valid
228.0ms	1487×	body	320	valid
189.0ms	4313×	body	80	valid
67.0ms	695×	body	160	valid