Details

analyze2.3s

Algorithm: search

sample57.0ms

Algorithm

intervals

Results

28.0ms	251×	body	80	valid
6.0ms	3×	body	640	valid
2.0ms	4×	body	1280	invalid
1.0ms	4×	body	320	invalid
1.0ms	8×	body	80	invalid
1.0ms	2×	body	640	invalid
1.0ms	1×	body	1280	valid
0.0ms	1×	body	160	valid

simplify49.0ms

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

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 17.0b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (neg (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)
37.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`add-cube-cbrt` `associate-r`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `associate-l`
4×	`add-log-exp`
3×	`pow-unpow` `associate-*r/` `exp-sum`
2×	`sub-neg` `cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `exp-diff` `pow-exp` `flip-+` `distribute-lft-out` `distribute-lft-out--` `associate--r-` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

29.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
6.0ms	(* K (+ m n))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series241.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
6.0ms	(* K (+ m n))
43.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify51.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	516	881
1	1857	790
2	5002	784

prune189.0ms

Filtered

62 candidates to 87 candidates (-40.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	5	88

Merged error: 1.0b

Counts

88 → 5

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`unpow-prod-down`
4×	`add-cube-cbrt` `add-log-exp` `difference-of-squares`
3×	`pow1` `add-exp-log` `pow-unpow`
2×	`times-frac` `add-cbrt-cube` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

2 → 35

Calls

2 calls:

10.0ms	(- (/ (+ m n) 2.0) M)
13.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series45.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(- (/ (+ m n) 2.0) M)
40.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify61.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	230	282
1	676	270
2	2402	264
3	5001	261

prune86.0ms

Filtered

30 candidates to 41 candidates (-36.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	41	5	46

Merged error: 1.0b

Counts

46 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
37.3b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 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 K)
1.0ms	(cbrt K)
1.0ms	(cbrt K)
14.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series94.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt K)
22.0ms	(cbrt K)
22.0ms	(cbrt K)
28.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify42.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (37.0ms)

Iter	Nodes	Cost
0	130	345
1	254	312
2	456	282
3	1079	279
4	5001	267

prune137.0ms

Filtered

43 candidates to 55 candidates (-27.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	55	5	60

Merged error: 1.0b

Counts

60 → 5

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
37.3b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (* (cbrt (* (cbrt K) (cbrt K))) (cbrt (cbrt K))) (+ m n))) 2.0) M))

rewrite21.0ms

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 K)
1.0ms	(cbrt K)
1.0ms	(cbrt K)
16.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (* (cbrt (* (cbrt K) (cbrt K))) (cbrt (cbrt K))) (+ m n))) 2.0) M))

series95.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt K)
22.0ms	(cbrt K)
22.0ms	(cbrt K)
29.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (* (cbrt (* (cbrt K) (cbrt K))) (cbrt (cbrt K))) (+ m n))) 2.0) M))

simplify61.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (56.0ms)

Iter	Nodes	Cost
0	135	441
1	304	396
2	761	366
3	2072	363
4	5001	354

prune105.0ms

Filtered

43 candidates to 55 candidates (-27.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	56	4	60

Merged error: 1.0b

Counts

60 → 4

regimes365.0ms

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

analyze2.3s

Algorithm: search

sample1.4s

Algorithm

intervals

Results

897.0ms	7824×	body	80	valid
53.0ms	87×	body	1280	invalid
38.0ms	86×	body	640	invalid
35.0ms	75×	body	640	valid
28.0ms	226×	body	80	invalid
26.0ms	40×	body	1280	valid
21.0ms	66×	body	320	invalid
14.0ms	42×	body	320	valid
7.0ms	30×	body	160	invalid
4.0ms	19×	body	160	valid

Details

analyze2.3s

sample57.0ms

simplify49.0ms

prune11.0ms

localize23.0ms

rewrite56.0ms

series241.0ms

simplify51.0ms

prune189.0ms

localize15.0ms

rewrite25.0ms

series45.0ms

simplify61.0ms

prune86.0ms

localize26.0ms

rewrite18.0ms

series94.0ms

simplify42.0ms

prune137.0ms

localize31.0ms

rewrite21.0ms

series95.0ms

simplify61.0ms

prune105.0ms

regimes365.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze2.3s

sample1.4s

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