Details

sample54.0ms

Algorithm

intervals

Results

32.0ms	259×	body	80	valid
2.0ms	5×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	4×	body	320	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	50	16
1	93	16
2	200	16
3	517	15
4	1893	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: 13.5b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.2b	(/ (* K (+ m n)) 2.0)
33.7b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-log-exp`
10×	`add-exp-log`
9×	`add-cube-cbrt` `add-cbrt-cube`
8×	`exp-prod`
7×	`distribute-lft-out--`
6×	`unpow-prod-down` `diff-log`
5×	`pow1` `rem-exp-log`
4×	`times-frac`
3×	`pow-unpow` `exp-sum` `associate-/r*` `difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `cos-sum` `distribute-rgt-neg-in` `associate-*r/` `div-exp` `neg-log` `associate-/l/`
1×	`cos-diff` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `exp-diff` `pow-exp` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*` `associate--r-` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

27.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
7.0ms	(/ (* K (+ m n)) 2.0)
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series506.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
279.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
48.0ms	(/ (* K (+ m n)) 2.0)
54.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify51.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	462	652
1	1789	592
2	5001	588

prune354.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	5	90

Merged error: 0.8b

Counts

90 → 5

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
24×	`add-log-exp`
15×	`add-sqr-sqrt`
13×	`distribute-lft-out--`
12×	`diff-log`
8×	`exp-prod`
6×	`add-cube-cbrt` `unpow-prod-down`
5×	`rem-exp-log`
4×	`pow1` `add-exp-log` `distribute-rgt-neg-in` `neg-log` `difference-of-squares`
3×	`sub-neg` `pow-unpow` `exp-sum` `add-cbrt-cube`
2×	`associate--r+` `associate--r-`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `times-frac` `exp-diff` `pow-exp` `flip--` `sqr-pow`

Counts

3 → 68

Calls

3 calls:

27.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
23.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series607.0ms

Counts

3 → 9

Calls

3 calls:

194.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
123.0ms	(exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
290.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	356	720
1	1112	675
2	5002	670

prune222.0ms

Filtered

77 candidates to 51 candidates (66.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	77	5	82

Merged error: 0.8b

Counts

82 → 5

localize35.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
33.7b	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
14.0ms	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

series215.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
215.0ms	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

simplify84.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	82	309
1	139	279
2	219	273
3	308	273
4	458	273
5	812	273
6	2301	273
7	5001	273

prune240.0ms

Filtered

49 candidates to 40 candidates (81.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	47	2	49
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	48	6	54

Merged error: 0.8b

Counts

54 → 6

localize36.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
33.7b	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))
33.7b	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))
33.7b	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cos-sum`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 41

Calls

4 calls:

1.0ms	(cbrt 2.0)
17.0ms	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))
15.0ms	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))
14.0ms	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

series639.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(cbrt 2.0)
209.0ms	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))
211.0ms	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))
218.0ms	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

simplify80.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	82	642
1	139	576
2	219	574
3	308	574
4	458	574
5	812	574
6	2301	574
7	5001	574

prune297.0ms

Filtered

51 candidates to 43 candidates (84.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	3	3
Picked	1	0	1
Done	1	1	2
Total	51	6	57

Merged error: 0.7b

Counts

57 → 6

regimes234.0ms

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

sample1.2s

Algorithm

intervals

Results

788.0ms	8105×	body	80	valid
58.0ms	144×	body	640	valid
55.0ms	98×	body	1280	valid
29.0ms	98×	body	320	valid
13.0ms	65×	body	160	valid

Details

sample54.0ms

simplify52.0ms

prune9.0ms

localize25.0ms

rewrite55.0ms

series506.0ms

simplify51.0ms

prune354.0ms

localize16.0ms

rewrite63.0ms

series607.0ms

simplify40.0ms

prune222.0ms

localize35.0ms

rewrite18.0ms

series215.0ms

simplify84.0ms

prune240.0ms

localize36.0ms

rewrite48.0ms

series639.0ms

simplify80.0ms

prune297.0ms

regimes234.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

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