Details

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 8.203125%

Guaranteed chance to sample good point: 72.340426%

Results

18.0ms	31×	body	1280	valid
18.0ms	45×	body	1280	invalid
18.0ms	53×	body	640	valid
12.0ms	125×	body	80	valid
9.0ms	33×	body	640	invalid
7.0ms	36×	body	320	valid
6.0ms	87×	body	80	invalid
5.0ms	23×	body	320	invalid
2.0ms	11×	body	160	valid
1.0ms	10×	body	160	invalid

simplify186.0ms

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	284	9
5	556	9
6	919	9
7	1220	9
8	3918	9
9	5002	9

prune4.0ms

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: 16.0b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0))) U)
0.0b	(* J (- (exp l) (exp (neg l))))
0.0b	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
5.1b	(- (exp l) (exp (neg l)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`associate-r` `add-log-exp`
7×	`add-cube-cbrt`
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×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

9.0ms	(+ (* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0))) U)
10.0ms	(* J (- (exp l) (exp (neg l))))
8.0ms	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (neg l)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0))) U)
10.0ms	(* J (- (exp l) (exp (neg l))))
22.0ms	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (neg l)))

simplify43.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	354	755
1	1430	660
2	5001	652

prune119.0ms

Filtered

58 candidates to 83 candidates (-43.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	2	84

Merged error: 0.1b

Counts

84 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

9.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
5.0ms	(* 1/60 (pow l 5))
6.0ms	(* 1/3 (pow l 3))
10.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
4.0ms	(* 1/60 (pow l 5))
4.0ms	(* 1/3 (pow l 3))
36.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

simplify73.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	464	817
1	2375	697
2	5001	697

prune209.0ms

Filtered

70 candidates to 110 candidates (-57.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	108	4	112

Merged error: 0.0b

Counts

112 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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:

5.0ms	(* 1/60 (pow l 5))
10.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
6.0ms	(* 1/3 (pow l 3))
10.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 1/60 (pow l 5))
39.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
4.0ms	(* 1/3 (pow l 3))
14.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

simplify66.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (13.0ms)

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

prune199.0ms

Filtered

69 candidates to 108 candidates (-56.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	108	4	112

Merged error: 0.0b

Counts

112 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/3 (pow l 3))
0.1b	(* 1/3 (pow l 3))
9.4b	(* J (- (* (* 1/3 (pow l 3)) (* 1/3 (pow l 3))) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
13.5b	(/ (* (* J (- (* (* 1/3 (pow l 3)) (* 1/3 (pow l 3))) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l))))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
28×	`associate-r`
25×	`add-exp-log`
19×	`add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
10×	`prod-exp`
9×	`associate-l` `unswap-sqr`
8×	`unpow-prod-down` `cube-prod`
6×	`pow1` `cbrt-unprod`
4×	`associate-*r/` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `flip3--` `times-frac` `div-exp` `associate-/r` `-commutative` `flip--`
2×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `distribute-lft-in` `unpow3` `associate-*l/` `pow-exp` `associate-/r/` `associate-/l/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `div-inv` `associate-/l*` `difference-of-squares`

Counts

4 → 114

Calls

4 calls:

6.0ms	(* 1/3 (pow l 3))
6.0ms	(* 1/3 (pow l 3))
11.0ms	(* J (- (* (* 1/3 (pow l 3)) (* 1/3 (pow l 3))) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
18.0ms	(/ (* (* J (- (* (* 1/3 (pow l 3)) (* 1/3 (pow l 3))) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l))))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

series156.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 1/3 (pow l 3))
4.0ms	(* 1/3 (pow l 3))
60.0ms	(* J (- (* (* 1/3 (pow l 3)) (* 1/3 (pow l 3))) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
89.0ms	(/ (* (* J (- (* (* 1/3 (pow l 3)) (* 1/3 (pow l 3))) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l))))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

simplify99.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	551	1783
1	3116	1455
2	5002	1454

prune435.0ms

Filtered

84 candidates to 126 candidates (-50.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	126	4	130

Merged error: 0.0b

Counts

130 → 4

regimes367.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b 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

sample5.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 8.203125%

Guaranteed chance to sample good point: 72.340426%

Results

709.0ms	1205×	body	1280	valid
599.0ms	1465×	body	1280	invalid
475.0ms	1373×	body	640	valid
352.0ms	1246×	body	640	invalid
289.0ms	4099×	body	80	valid
198.0ms	2855×	body	80	invalid
194.0ms	895×	body	320	valid
119.0ms	593×	body	320	invalid
60.0ms	428×	body	160	valid
44.0ms	321×	body	160	invalid

Details

sample1.8s

simplify186.0ms

prune4.0ms

localize13.0ms

rewrite34.0ms

series83.0ms

simplify43.0ms

prune119.0ms

localize17.0ms

rewrite35.0ms

series67.0ms

simplify73.0ms

prune209.0ms

localize21.0ms

rewrite33.0ms

series60.0ms

simplify66.0ms

prune199.0ms

localize26.0ms

rewrite44.0ms

series156.0ms

simplify99.0ms

prune435.0ms

regimes367.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.3s

Profiling