Details

sample42.0ms

Algorithm

intervals

Results

20.0ms	252×	body	80	valid
3.0ms	8×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	2×	body	1280	valid
1.0ms	1×	body	2560	valid
0.0ms	1×	body	160	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	15
5	5001	15

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 16.9b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
38.0b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

198×	`add-sqr-sqrt`
167×	`*-un-lft-identity`
150×	`prod-diff`
81×	`add-cube-cbrt`
78×	`unpow-prod-down`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
51×	`difference-of-squares`
43×	`distribute-lft-out--`
24×	`fma-neg`
23×	`cos-sum`
22×	`times-frac`
14×	`add-log-exp`
13×	`sqr-pow`
11×	`associate--r+`
7×	`pow1` `add-exp-log`
6×	`neg-mul-1` `diff-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`sub-neg` `pow-unpow` `associate-l` `div-inv`
2×	`associate-*r/` `neg-log`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr`

Counts

4 → 259

Calls

4 calls:

6.0ms	(* K (+ m n))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
26.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
11.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series510.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* K (+ m n))
253.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
176.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify106.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	991	6064
1	2883	4404
2	5001	4329

prune630.0ms

Filtered

271 candidates to 116 candidates (42.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	265	6	271
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	266	6	272

Merged error: 1.6b

Counts

272 → 6

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
148×	`*-un-lft-identity`
129×	`prod-diff`
78×	`unpow-prod-down`
64×	`add-cube-cbrt`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
51×	`difference-of-squares`
43×	`distribute-lft-out--`
24×	`fma-neg`
13×	`times-frac` `sqr-pow`
12×	`add-log-exp`
11×	`associate--r+`
6×	`neg-mul-1` `diff-log`
3×	`pow1` `add-exp-log` `pow-unpow`
2×	`expm1-log1p-u` `sub-neg` `neg-log` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `flip--` `associate--r-`

Counts

2 → 201

Calls

2 calls:

11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
30.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series465.0ms

Counts

2 → 6

Calls

2 calls:

286.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
178.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify79.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	608	5050
1	1693	3609
2	5001	3001

prune333.0ms

Filtered

207 candidates to 71 candidates (34.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	207	6	213

Merged error: 1.6b

Counts

213 → 6

localize41.0ms

Local error

Found 4 expressions with local error:

17.0b	(cbrt (* K (+ m n)))
17.0b	(cbrt (* K (+ m n)))
17.0b	(cbrt (* K (+ m n)))
38.2b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cos-sum`
21×	`prod-diff`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`cbrt-div` `associate-*r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+` `div-inv`
1×	`cos-diff` `sub-neg`

Counts

4 → 72

Calls

4 calls:

5.0ms	(cbrt (* K (+ m n)))
5.0ms	(cbrt (* K (+ m n)))
5.0ms	(cbrt (* K (+ m n)))
13.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series361.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (* K (+ m n)))
101.0ms	(cbrt (* K (+ m n)))
101.0ms	(cbrt (* K (+ m n)))
58.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify59.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	426	1888
1	786	1586
2	1878	1562
3	5002	1391

prune360.0ms

Filtered

84 candidates to 60 candidates (71.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	84	6	90

Merged error: 1.5b

Counts

90 → 6

localize35.0ms

Local error

Found 4 expressions with local error:

17.0b	(cbrt (* K (+ m n)))
17.0b	(cbrt (* K (+ m n)))
17.0b	(cbrt (* K (+ m n)))
38.2b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n)))))) 2.0) M))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cos-sum`
21×	`prod-diff`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`cbrt-div` `associate-*r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+` `div-inv`
1×	`cos-diff` `sub-neg`

Counts

4 → 72

Calls

4 calls:

5.0ms	(cbrt (* K (+ m n)))
5.0ms	(cbrt (* K (+ m n)))
5.0ms	(cbrt (* K (+ m n)))
25.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n)))))) 2.0) M))

series370.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(cbrt (* K (+ m n)))
103.0ms	(cbrt (* K (+ m n)))
104.0ms	(cbrt (* K (+ m n)))
59.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n)))))) 2.0) M))

simplify75.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	441	2746
1	865	2356
2	2322	2332
3	5001	2029

prune413.0ms

Filtered

84 candidates to 60 candidates (71.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	83	7	90

Merged error: 1.5b

Counts

90 → 7

regimes274.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	23	10
2	23	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

669.0ms	8117×	body	80	valid
52.0ms	152×	body	640	valid
49.0ms	98×	body	1280	valid
25.0ms	99×	body	320	valid
11.0ms	47×	body	160	valid
3.0ms	4×	body	2560	valid