Details

sample40.0ms

Algorithm

intervals

Results

17.0ms	383×	body	80	valid
6.0ms	159×	body	80	nan

simplify110.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	24	7
1	48	7
2	96	6
3	256	6
4	891	6
5	3954	6
6	5002	6

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 1.3b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (pow k m))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(+ 1.0 (* 10.0 k))
1.3b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

3×	`+-commutative` `flip3-+` `flip-+` `associate-/l*`
2×	`associate-+l+` `associate-r` `associate-/r/` `*-commutative` `sqr-pow`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 18

Calls

4 calls:

3.0ms	(* a (pow k m))
5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
3.0ms	(+ 1.0 (* 10.0 k))
10.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* a (pow k m))
18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
32.0ms	(+ 1.0 (* 10.0 k))
114.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify95.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	266	217
1	939	209
2	3880	182
3	5001	178

prune76.0ms

Filtered

30 candidates to 21 candidates (70.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	29	3	32

Merged error: 1.3b

Counts

32 → 3

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(* a (pow k m))
1.3b	(/ (* a (pow k m)) (+ (* 10.0 k) (+ (pow k 2) 1.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-/l*`
2×	`associate-r` `associate-/r/` `*-commutative` `sqr-pow`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv`

Counts

2 → 10

Calls

2 calls:

3.0ms	(* a (pow k m))
7.0ms	(/ (* a (pow k m)) (+ (* 10.0 k) (+ (pow k 2) 1.0)))

series177.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(* a (pow k m))
116.0ms	(/ (* a (pow k m)) (+ (* 10.0 k) (+ (pow k 2) 1.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	202	147
1	676	146
2	2837	131
3	5002	127

prune59.0ms

Filtered

16 candidates to 13 candidates (81.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	13	3	16
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	16	3	19

Merged error: 1.3b

Counts

19 → 3

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
1.3b	(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (* 10.0 k) (+ (pow k 2) 1.0)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`associate-l` `associate-/l*`
4×	`associate-r` `*-commutative` `sqr-pow`
2×	`associate-/r/`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv`

Counts

2 → 16

Calls

2 calls:

4.0ms	(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
10.0ms	(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (* 10.0 k) (+ (pow k 2) 1.0)))

series217.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
143.0ms	(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (* 10.0 k) (+ (pow k 2) 1.0)))

simplify110.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	233	225
1	877	212
2	4062	205
3	5001	205

prune91.0ms

Filtered

22 candidates to 20 candidates (90.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	21	4	25

Merged error: 0.0b

Counts

25 → 4

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ (* 10.0 k) (+ (pow k 2) 1.0)) (* (pow k (/ (/ m 2) 2)) (pow k (/ m 2))))
1.3b	(/ (* a (pow k (/ (/ m 2) 2))) (/ (+ (* 10.0 k) (+ (pow k 2) 1.0)) (* (pow k (/ (/ m 2) 2)) (pow k (/ m 2)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

11×	`associate-/r*`
10×	`associate-/r/` `sqr-pow`
6×	`div-inv`
4×	`associate-r` `*-commutative` `associate-/l/`
3×	`frac-2neg` `times-frac` `clear-num` `associate-/l*`
2×	`flip3-+` `associate-l` `flip-+` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

9.0ms	(/ (+ (* 10.0 k) (+ (pow k 2) 1.0)) (* (pow k (/ (/ m 2) 2)) (pow k (/ m 2))))
14.0ms	(/ (* a (pow k (/ (/ m 2) 2))) (/ (+ (* 10.0 k) (+ (pow k 2) 1.0)) (* (pow k (/ (/ m 2) 2)) (pow k (/ m 2)))))

series336.0ms

Counts

2 → 6

Calls

2 calls:

123.0ms	(/ (+ (* 10.0 k) (+ (pow k 2) 1.0)) (* (pow k (/ (/ m 2) 2)) (pow k (/ m 2))))
212.0ms	(/ (* a (pow k (/ (/ m 2) 2))) (/ (+ (* 10.0 k) (+ (pow k 2) 1.0)) (* (pow k (/ (/ m 2) 2)) (pow k (/ m 2)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	422	586
1	1699	546
2	5002	532

prune147.0ms

Filtered

36 candidates to 34 candidates (94.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	34	2	36
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	36	4	40

Merged error: 0.0b

Counts

40 → 4

regimes94.0ms

Accuracy

98.5% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 1.9b

bsearch69.0ms

Steps

Iters	Range		Point
8	2.780302897405976e+149	1.3412804874082685e+153	3.2205424189704093e+149

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	44
1	61	44

end0.0ms

sample1.1s

Algorithm

intervals

Results

545.0ms	11880×	body	80	valid
164.0ms	4240×	body	80	nan