Details

sample47.0ms

Algorithm

intervals

Results

24.0ms	259×	body	80	valid
2.0ms	6×	body	640	valid
2.0ms	3×	body	1280	valid
1.0ms	4×	body	320	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	15
5	5001	15

prune13.0ms

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: 15.1b

Counts

2 → 1

localize21.0ms

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)
35.3b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite51.0ms

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))
20.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
11.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series510.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* K (+ m n))
174.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
258.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
54.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify69.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (50.0ms)

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

prune451.0ms

Filtered

130 candidates to 88 candidates (67.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	125	5	130
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	5	131

Merged error: 1.6b

Counts

131 → 5

localize14.0ms

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

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:

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

series560.0ms

Counts

2 → 6

Calls

2 calls:

170.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
390.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify120.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (26.0ms)

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

prune208.0ms

Filtered

66 candidates to 50 candidates (75.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	66	5	71

Merged error: 1.6b

Counts

71 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
35.6b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
23×	`cos-sum`
21×	`prod-diff`
20×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`cbrt-prod`
9×	`times-frac`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `div-inv` `distribute-lft-out`
1×	`cos-diff` `sub-neg`

Counts

4 → 81

Calls

4 calls:

3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
18.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series469.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (+ m n))
121.0ms	(cbrt (+ m n))
121.0ms	(cbrt (+ m n))
100.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify90.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	427	1747
1	906	1467
2	3154	1458
3	5001	1308

prune386.0ms

Filtered

93 candidates to 63 candidates (67.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	90	8	98

Merged error: 1.6b

Counts

98 → 8

localize48.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
35.3b	(sin (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt 2.0) (cbrt 2.0))) (/ (cbrt (+ m n)) (cbrt 2.0)) (- (* M 1))))
35.6b	(cos (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt 2.0) (cbrt 2.0))) (/ (cbrt (+ 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	(sin (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt 2.0) (cbrt 2.0))) (/ (cbrt (+ m n)) (cbrt 2.0)) (- (* M 1))))
2.0ms	(cos (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt 2.0) (cbrt 2.0))) (/ (cbrt (+ m n)) (cbrt 2.0)) (- (* M 1))))

series669.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
337.0ms	(sin (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt 2.0) (cbrt 2.0))) (/ (cbrt (+ m n)) (cbrt 2.0)) (- (* M 1))))
332.0ms	(cos (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt 2.0) (cbrt 2.0))) (/ (cbrt (+ m n)) (cbrt 2.0)) (- (* M 1))))

simplify60.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	162	742
1	376	660
2	904	656
3	2287	654
4	5001	654

prune419.0ms

Filtered

54 candidates to 46 candidates (85.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	5	5
Picked	0	1	1
Done	1	1	2
Total	53	9	62

Merged error: 1.6b

Counts

62 → 9

regimes372.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

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

793.0ms	8086×	body	80	valid
77.0ms	136×	body	1280	valid
73.0ms	180×	body	640	valid
29.0ms	99×	body	320	valid
8.0ms	40×	body	160	valid