Details

sample59.0ms

Algorithm

intervals

Results

27.0ms	255×	body	80	valid
4.0ms	7×	body	1280	valid
2.0ms	6×	body	320	valid
1.0ms	3×	body	640	valid
0.0ms	1×	body	160	valid

simplify50.0ms

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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 17.2b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
0.2b	(/ (* K (+ m n)) 2.0)
35.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

14.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms	(* K (+ m n))
7.0ms	(/ (* K (+ m n)) 2.0)
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series381.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
25.0ms	(* K (+ m n))
44.0ms	(/ (* K (+ m n)) 2.0)
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify48.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	411	487
1	1722	437
2	5001	437

prune324.0ms

Filtered

88 candidates to 63 candidates (71.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 1.4b

Counts

89 → 4

localize19.0ms

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)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

17.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series436.0ms

Counts

2 → 6

Calls

2 calls:

175.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
261.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify74.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	253	368
1	720	351
2	2937	346
3	5001	343

prune128.0ms

Filtered

43 candidates to 31 candidates (72.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	43	4	47

Merged error: 1.4b

Counts

47 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
35.4b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 52

Calls

4 calls:

3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
20.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series481.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt (+ m n))
131.0ms	(cbrt (+ m n))
124.0ms	(cbrt (+ m n))
101.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify153.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (146.0ms)

Iter	Nodes	Cost
0	186	485
1	416	445
2	1213	439
3	4532	439
4	5003	433

prune327.0ms

Filtered

64 candidates to 52 candidates (81.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	61	7	68

Merged error: 1.4b

Counts

68 → 7

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
0.7b	(pow (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M)) 3)
35.4b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`cbrt-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cbrt-div` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
2×	`cos-sum` `flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`cos-diff` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
3.0ms	(pow (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M)) 3)
17.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series506.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(cbrt (+ m n))
122.0ms	(cbrt (+ m n))
153.0ms	(pow (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M)) 3)
101.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify155.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	251	811
1	768	724
2	4193	716
3	5001	716

prune311.0ms

Filtered

73 candidates to 52 candidates (71.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	73	7	80

Merged error: 1.4b

Counts

80 → 7

regimes255.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

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

859.0ms	8126×	body	80	valid
70.0ms	110×	body	1280	valid
67.0ms	151×	body	640	valid
36.0ms	113×	body	320	valid
14.0ms	67×	body	160	valid
1.0ms	1×	body	2560	valid

Details

sample59.0ms

simplify50.0ms

prune9.0ms

localize23.0ms

rewrite38.0ms

series381.0ms

simplify48.0ms

prune324.0ms

localize19.0ms

rewrite29.0ms

series436.0ms

simplify74.0ms

prune128.0ms

localize26.0ms

rewrite31.0ms

series481.0ms

simplify153.0ms

prune327.0ms

localize36.0ms

rewrite29.0ms

series506.0ms

simplify155.0ms

prune311.0ms

regimes255.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling