Details

sample115.0ms

Algorithm

intervals

Results

35.0ms	88×	body	1280	valid
22.0ms	87×	body	640	valid
21.0ms	312×	body	80	valid
12.0ms	67×	body	320	valid
3.0ms	26×	body	160	valid

simplify372.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	9
1	41	9
2	83	9
3	173	9
4	271	9
5	533	9
6	1023	9
7	1395	9
8	4369	9
9	5002	9

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: 17.5b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.9b	(- (exp l) (exp (- l)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

8.0ms	(* J (- (exp l) (exp (- l))))
10.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (- l)))

series179.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* J (- (exp l) (exp (- l))))
89.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
39.0ms	(- (exp l) (exp (- l)))

simplify37.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	264	566
1	1116	481
2	5002	475

prune214.0ms

Filtered

69 candidates to 47 candidates (68.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	2	70

Merged error: 0.0b

Counts

70 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
0.1b	(* 1/60 (pow l 5))
0.1b	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
0.1b	(* 1/3 (pow l 3))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
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×	`pow-prod-down` `*-commutative`
2×	`pow-to-exp` `flip3-+` `associate-r/` `associate-l/` `pow-exp` `flip-+`
1×	`+-commutative` `cube-mult` `unpow3` `sum-log`

Counts

4 → 87

Calls

4 calls:

11.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
5.0ms	(* 1/60 (pow l 5))
11.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
9.0ms	(* 1/3 (pow l 3))

series571.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
50.0ms	(* 1/60 (pow l 5))
163.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
35.0ms	(* 1/3 (pow l 3))

simplify74.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	465	784
1	2234	701
2	5003	701

prune344.0ms

Filtered

99 candidates to 65 candidates (65.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	94	7	101

Merged error: 0.0b

Counts

101 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`associate-r`
21×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-l`
11×	`pow1`
10×	`prod-exp`
8×	`unpow-prod-down` `unswap-sqr`
6×	`cbrt-unprod`
4×	`cube-prod` `pow-prod-down` `associate-l/` `-commutative` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `flip-+`
1×	`cube-mult` `unpow3`

Counts

4 → 96

Calls

4 calls:

11.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
5.0ms	(* 1/60 (pow l 5))
7.0ms	(* 1/3 (pow l 3))
10.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
46.0ms	(* 1/60 (pow l 5))
40.0ms	(* 1/3 (pow l 3))
87.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	444	856
1	2079	731
2	5001	731

prune382.0ms

Filtered

108 candidates to 69 candidates (63.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	2	3	5
Picked	0	1	1
Done	1	0	1
Total	108	7	115

Merged error: 0.0b

Counts

115 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/3 (pow l 3))
3.2b	(* J (* (pow l 6) 1/9))
7.2b	(* J (- (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
13.8b	(/ (* (cos (/ K 2.0)) (+ (* J (* (pow l 6) 1/9)) (* J (- (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l))))))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

6.0ms	(* 1/3 (pow l 3))
6.0ms	(* J (* (pow l 6) 1/9))
8.0ms	(* J (- (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
14.0ms	(/ (* (cos (/ K 2.0)) (+ (* J (* (pow l 6) 1/9)) (* J (- (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l))))))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

series1.2s

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 1/3 (pow l 3))
100.0ms	(* J (* (pow l 6) 1/9))
404.0ms	(* J (- (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
619.0ms	(/ (* (cos (/ K 2.0)) (+ (* J (* (pow l 6) 1/9)) (* J (- (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l))))))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

simplify145.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (129.0ms)

Iter	Nodes	Cost
0	811	1644
1	4570	1403
2	5001	1402

prune555.0ms

Filtered

121 candidates to 80 candidates (66.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	122	6	128

Merged error: 0b

Counts

128 → 6

regimes254.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	12
1	30	12

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.1s	2630×	body	1280	valid
905.0ms	2593×	body	640	valid
466.0ms	8418×	body	80	valid
265.0ms	1459×	body	320	valid
88.0ms	713×	body	160	valid