Details

sample48.0ms

Algorithm

intervals

Results

25.0ms	255×	body	80	valid
3.0ms	5×	body	1280	valid
2.0ms	4×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	1×	body	2560	valid

simplify48.0ms

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 (100.0%)

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: 13.5b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ 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)
35.0b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite50.0ms

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:

12.0ms	(* K (+ m n))
18.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series520.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* K (+ m n))
170.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
254.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
72.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	411	566
1	1369	528
2	5001	523

prune283.0ms

Filtered

82 candidates to 58 candidates (70.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	3	83

Merged error: 1.0b

Counts

83 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
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)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
13×	`times-frac`
11×	`add-log-exp`
6×	`pow1` `add-exp-log` `unpow-prod-down` `pow-flip` `add-cbrt-cube`
5×	`exp-prod`
4×	`exp-sum` `associate-/r*` `distribute-lft-out` `distribute-lft-out--`
3×	`pow-unpow` `associate-/l*` `difference-of-squares`
2×	`associate-+r-` `sub-neg` `associate-+r+` `diff-log` `div-exp` `sum-log`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rec-exp` `flip3--` `pow-pow` `frac-2neg` `flip3-+` `exp-diff` `1-exp` `pow-exp` `clear-num` `associate-/r/` `flip--` `flip-+` `div-inv` `inv-pow` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

24.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
3.0ms	(- l (fabs (- m n)))
16.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series597.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
11.0ms	(- l (fabs (- m n)))
169.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
261.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	453	1091
1	1648	1020
2	5001	1000

prune242.0ms

Filtered

104 candidates to 65 candidates (62.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	104	3	107

Merged error: 1.0b

Counts

107 → 3

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
34.7b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite19.0ms

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))

series633.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt K)
173.0ms	(cbrt K)
184.0ms	(cbrt K)
102.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify97.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	111	309
1	265	279
2	681	273
3	3070	273
4	5001	273

prune265.0ms

Filtered

55 candidates to 46 candidates (83.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	52	3	55
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	54	4	58

Merged error: 0.9b

Counts

58 → 4

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
34.7b	(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))

series633.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt K)
181.0ms	(cbrt K)
175.0ms	(cbrt K)
101.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify97.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	111	309
1	265	279
2	681	273
3	3070	273
4	5001	273

prune273.0ms

Filtered

55 candidates to 47 candidates (85.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	55	4	59

Merged error: 0.9b

Counts

59 → 4

regimes172.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b 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

sample1.3s

Algorithm

intervals

Results

809.0ms	8084×	body	80	valid
78.0ms	124×	body	1280	valid
71.0ms	164×	body	640	valid
32.0ms	105×	body	320	valid
13.0ms	64×	body	160	valid
6.0ms	7×	body	2560	valid

Details

sample48.0ms

simplify48.0ms

prune12.0ms

localize20.0ms

rewrite50.0ms

series520.0ms

simplify42.0ms

prune283.0ms

localize14.0ms

rewrite57.0ms

series597.0ms

simplify50.0ms

prune242.0ms

localize25.0ms

rewrite19.0ms

series633.0ms

simplify97.0ms

prune265.0ms

localize34.0ms

rewrite20.0ms

series633.0ms

simplify97.0ms

prune273.0ms

regimes172.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling