Details

sample55.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
4.0ms	7×	body	1280	valid
3.0ms	6×	body	640	valid
1.0ms	2×	body	320	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

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 14.5b

Counts

2 → 1

localize213.0ms

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)
32.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

18.0ms	(+ (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)
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series112.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (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)
21.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	442	576
1	1444	538
2	5002	530

prune177.0ms

Filtered

82 candidates to 58 candidates (29.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	6	83

Merged error: 1.6b

Counts

83 → 6

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

3.0ms	(- l (fabs (- m n)))
17.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series86.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(- l (fabs (- m n)))
40.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
42.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify86.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	325	466
1	873	449
2	3345	441
3	5001	438

prune114.0ms

Filtered

60 candidates to 42 candidates (30.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	60	6	66

Merged error: 1.6b

Counts

66 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
32.1b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite20.0ms

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

series94.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt K)
23.0ms	(cbrt K)
22.0ms	(cbrt K)
27.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify44.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (39.0ms)

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

prune134.0ms

Filtered

55 candidates to 43 candidates (21.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	50	5	55
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	54	7	61

Merged error: 1.5b

Counts

61 → 7

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.7b	(cbrt (* (cbrt K) (cbrt K)))
32.2b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (* (cbrt (* (cbrt K) (cbrt K))) (cbrt (cbrt K))) (+ m n))) 2.0) M))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

7×	`cbrt-prod`
6×	`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 → 41

Calls

4 calls:

1.0ms	(cbrt K)
1.0ms	(cbrt K)
4.0ms	(cbrt (* (cbrt K) (cbrt K)))
16.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (* (cbrt (* (cbrt K) (cbrt K))) (cbrt (cbrt K))) (+ m n))) 2.0) M))

series108.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt K)
21.0ms	(cbrt K)
37.0ms	(cbrt (* (cbrt K) (cbrt K)))
28.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (* (cbrt (* (cbrt K) (cbrt K))) (cbrt (cbrt K))) (+ m n))) 2.0) M))

simplify47.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	190	468
1	430	417
2	1277	385
3	5001	375

prune102.0ms

Filtered

53 candidates to 42 candidates (20.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	53	7	60

Merged error: 1.5b

Counts

60 → 7

regimes459.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

sample1.5s

Algorithm

intervals

Results

809.0ms	8091×	body	80	valid
76.0ms	128×	body	1280	valid
71.0ms	166×	body	640	valid
30.0ms	96×	body	320	valid
12.0ms	58×	body	160	valid
1.0ms	1×	body	2560	valid

Details

sample55.0ms

simplify49.0ms

prune12.0ms

localize213.0ms

rewrite45.0ms

series112.0ms

simplify44.0ms

prune177.0ms

localize14.0ms

rewrite32.0ms

series86.0ms

simplify86.0ms

prune114.0ms

localize25.0ms

rewrite20.0ms

series94.0ms

simplify44.0ms

prune134.0ms

localize33.0ms

rewrite23.0ms

series108.0ms

simplify47.0ms

prune102.0ms

regimes459.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.5s

Profiling