Details

sample49.0ms

Algorithm

intervals

Results

25.0ms	261×	body	80	valid
3.0ms	6×	body	640	valid
2.0ms	4×	body	1280	valid
1.0ms	1×	body	2560	valid
1.0ms	3×	body	320	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	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: 15.7b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
32.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`prod-diff`
29×	`add-cube-cbrt`
23×	`cos-sum`
12×	`unpow-prod-down`
11×	`associate-+r+` `times-frac`
10×	`fma-def`
9×	`add-log-exp`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `difference-of-squares`
3×	`pow-unpow` `associate-l` `div-inv` `distribute-lft-out` `distribute-lft-out--`
2×	`sub-neg` `flip3-+` `associate-*r/` `sum-log` `flip-+` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `cos-diff` `pow-to-exp` `associate-+r-` `pow-pow` `distribute-lft-in` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

6.0ms	(* K (+ m n))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
18.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
12.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series524.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* K (+ m n))
265.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
177.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify64.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	709	1542
1	2139	1259
2	5001	1252

prune441.0ms

Filtered

130 candidates to 88 candidates (67.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	126	4	130
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	4	131

Merged error: 0.8b

Counts

131 → 4

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
12×	`add-cube-cbrt` `unpow-prod-down`
11×	`associate-+r+`
10×	`fma-def`
9×	`prod-diff`
7×	`add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `pow-unpow` `distribute-lft-out--`
2×	`expm1-log1p-u` `times-frac` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `sub-neg` `pow-pow` `flip3-+` `diff-log` `pow-exp` `flip-+`

Counts

2 → 60

Calls

2 calls:

15.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
18.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

series445.0ms

Counts

2 → 6

Calls

2 calls:

265.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
180.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

simplify128.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	326	528
1	945	464
2	4380	448
3	5001	448

prune212.0ms

Filtered

66 candidates to 50 candidates (75.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	66	4	70

Merged error: 0.8b

Counts

70 → 4

localize39.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
32.8b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
32.9b	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`
1×	`cos-sum` `sin-sum`

Counts

4 → 46

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
2.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
2.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

series426.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
208.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
218.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify117.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	162	536
1	394	479
2	986	470
3	2961	468
4	5003	468

prune405.0ms

Filtered

54 candidates to 47 candidates (87.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	53	5	58

Merged error: 0.8b

Counts

58 → 5

localize51.0ms

Local error

Found 4 expressions with local error:

32.8b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
32.8b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
32.8b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
32.9b	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`
3×	`cos-sum`
1×	`sin-sum`

Counts

4 → 40

Calls

4 calls:

2.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
2.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
2.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
2.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

series837.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
211.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
206.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
210.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify57.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	108	754
1	251	653
2	596	652
3	1348	652
4	5002	652

prune443.0ms

Filtered

52 candidates to 48 candidates (92.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	52	5	57

Merged error: 0.8b

Counts

57 → 5

regimes206.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.2b and baseline of 1.3b

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

804.0ms	8088×	body	80	valid
69.0ms	114×	body	1280	valid
66.0ms	158×	body	640	valid
33.0ms	112×	body	320	valid
10.0ms	49×	body	160	valid
3.0ms	3×	body	2560	valid