Details

sample44.0ms

Algorithm

intervals

Results

22.0ms	265×	body	80	valid
2.0ms	8×	body	320	valid
1.0ms	3×	body	640	valid
1.0ms	2×	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

prune15.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 16.8b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- l (fabs (- m n)))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.2b	(/ (* K (+ m n)) 2.0)
35.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

3.0ms	(- l (fabs (- m n)))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
7.0ms	(/ (* K (+ m n)) 2.0)
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series381.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- l (fabs (- m n)))
271.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
41.0ms	(/ (* K (+ m n)) 2.0)
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify50.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	402	496
1	1506	449
2	5002	448

prune329.0ms

Filtered

79 candidates to 58 candidates (73.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Merged error: 0.8b

Counts

81 → 4

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	(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)

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

21.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
18.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
3.0ms	(- l (fabs (- m n)))
14.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series574.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
120.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
12.0ms	(- l (fabs (- m n)))
272.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	420	1098
1	1465	1017
2	5001	992

prune326.0ms

Filtered

104 candidates to 66 candidates (63.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	104	4	108

Merged error: 0.8b

Counts

108 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

3.0ms	(- l (fabs (- m n)))
3.0ms	(- l (fabs (- m n)))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
15.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series585.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- l (fabs (- m n)))
12.0ms	(- l (fabs (- m n)))
279.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
281.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	214	518
1	546	494
2	1696	492
3	5002	486

prune373.0ms

Filtered

80 candidates to 56 candidates (70.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	80	4	84

Merged error: 0.8b

Counts

84 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
35.1b	(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))

series208.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
208.0ms	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

simplify77.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (6.0ms)

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

prune250.0ms

Filtered

49 candidates to 41 candidates (83.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	47	2	49
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	48	5	53

Merged error: 0.8b

Counts

53 → 5

regimes195.0ms

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	22	23
1	22	23

end0.0ms

sample1.2s

Algorithm

intervals

Results

720.0ms	8160×	body	80	valid
62.0ms	157×	body	640	valid
62.0ms	117×	body	1280	valid
30.0ms	108×	body	320	valid
9.0ms	49×	body	160	valid
3.0ms	4×	body	2560	valid