Details

sample48.0ms

Algorithm

intervals

Results

25.0ms	261×	body	80	valid
3.0ms	8×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify50.0ms

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: 16.0b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite70.0ms

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:

25.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
6.0ms	(* K (+ m n))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
11.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series543.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
32.0ms	(* K (+ m n))
271.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify112.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 2 (69.0ms)

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

prune624.0ms

Filtered

271 candidates to 116 candidates (42.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	267	4	271
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	268	4	272

Merged error: 1.1b

Counts

272 → 4

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite53.0ms

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:

25.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
12.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series450.0ms

Counts

2 → 6

Calls

2 calls:

183.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
266.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify78.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (44.0ms)

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

prune310.0ms

Filtered

207 candidates to 71 candidates (34.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	206	5	211

Merged error: 1.1b

Counts

211 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.3b	(log1p (expm1 (cos (- (/ (* K (+ m n)) 2.0) M))))
0.3b	(expm1 (cos (- (/ (* K (+ m n)) 2.0) M)))
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
23×	`cos-sum`
21×	`*-un-lft-identity` `prod-diff`
19×	`add-cube-cbrt`
10×	`times-frac`
6×	`unpow-prod-down`
5×	`pow1` `add-exp-log` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`difference-of-squares`
1×	`cos-diff` `pow-to-exp` `sub-neg` `log1p-udef` `expm1-log1p` `pow-pow` `log1p-expm1` `pow-exp` `distribute-lft-out--` `expm1-udef` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.0ms	(log1p (expm1 (cos (- (/ (* K (+ m n)) 2.0) M))))
1.0ms	(expm1 (cos (- (/ (* K (+ m n)) 2.0) M)))
11.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series517.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
96.0ms	(log1p (expm1 (cos (- (/ (* K (+ m n)) 2.0) M))))
106.0ms	(expm1 (cos (- (/ (* K (+ m n)) 2.0) M)))
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify101.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	466	1294
1	1059	1055
2	3521	1053
3	5001	989

prune319.0ms

Filtered

89 candidates to 55 candidates (61.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	89	5	94

Merged error: 1.1b

Counts

94 → 5

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(expm1 (cos (- (/ (* K (+ m n)) 2.0) M)))
0.6b	(cbrt (pow (expm1 (cos (- (/ (* K (+ m n)) 2.0) M))) 3))
0.8b	(pow (expm1 (cos (- (/ (* K (+ m n)) 2.0) M))) 3)
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt` `add-cube-cbrt` `cos-sum` `*-un-lft-identity`
21×	`prod-diff`
12×	`cbrt-prod`
9×	`times-frac`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`cos-diff` `pow-to-exp` `sub-neg` `expm1-log1p` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `expm1-udef` `rem-cube-cbrt`

Counts

4 → 92

Calls

4 calls:

1.0ms	(expm1 (cos (- (/ (* K (+ m n)) 2.0) M)))
2.0ms	(cbrt (pow (expm1 (cos (- (/ (* K (+ m n)) 2.0) M))) 3))
2.0ms	(pow (expm1 (cos (- (/ (* K (+ m n)) 2.0) M))) 3)
12.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series526.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(expm1 (cos (- (/ (* K (+ m n)) 2.0) M)))
105.0ms	(cbrt (pow (expm1 (cos (- (/ (* K (+ m n)) 2.0) M))) 3))
256.0ms	(pow (expm1 (cos (- (/ (* K (+ m n)) 2.0) M))) 3)
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify168.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	405	1551
1	960	1303
2	4355	1297
3	5001	1297

prune347.0ms

Filtered

104 candidates to 55 candidates (52.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	103	6	109

Merged error: 1.1b

Counts

109 → 6

regimes219.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.3s

Algorithm

intervals

Results

809.0ms	8095×	body	80	valid
72.0ms	160×	body	640	valid
72.0ms	126×	body	1280	valid
33.0ms	112×	body	320	valid
13.0ms	61×	body	160	valid
3.0ms	3×	body	2560	valid