Details

sample52.0ms

Algorithm

intervals

Results

25.0ms	250×	body	80	valid
3.0ms	8×	body	640	valid
2.0ms	4×	body	1280	valid
2.0ms	8×	body	320	valid
1.0ms	3×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

Iter	Nodes	Cost
0	50	16
1	93	16
2	200	16
3	517	15
4	1893	15
5	5001	15

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 16.9b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
15×	`add-log-exp`
9×	`add-cube-cbrt`
8×	`exp-prod`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`unpow-prod-down` `diff-log` `add-cbrt-cube`
5×	`rem-exp-log`
4×	`exp-diff` `associate-r`
3×	`sub-neg` `pow-unpow` `associate-l` `exp-sum` `difference-of-squares`
2×	`+-commutative` `distribute-rgt-in` `cos-sum` `distribute-rgt-neg-in` `distribute-lft-in` `associate-*r/` `neg-log` `associate--r+`
1×	`associate--l-` `neg-sub0` `cos-diff` `pow-to-exp` `pow-pow` `flip3-+` `times-frac` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr` `sqr-pow`

Counts

4 → 82

Calls

4 calls:

6.0ms	(* K (+ m n))
23.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
13.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
23.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series510.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* K (+ m n))
133.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
283.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
61.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify50.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	443	648
1	1486	602
2	5001	597

prune327.0ms

Filtered

94 candidates to 65 candidates (69.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 2.8b

Counts

95 → 9

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
24×	`add-log-exp`
15×	`add-sqr-sqrt`
13×	`distribute-lft-out--`
12×	`diff-log`
8×	`exp-prod`
6×	`add-cube-cbrt` `unpow-prod-down`
5×	`rem-exp-log`
4×	`pow1` `add-exp-log` `sub-neg` `distribute-rgt-neg-in` `exp-diff` `neg-log` `associate--r+` `difference-of-squares`
3×	`pow-unpow` `exp-sum` `add-cbrt-cube`
2×	`associate--l-` `neg-sub0` `associate--r-`
1×	`pow-to-exp` `flip3--` `pow-pow` `times-frac` `pow-exp` `flip--` `sqr-pow`

Counts

3 → 71

Calls

3 calls:

21.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
22.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series598.0ms

Counts

3 → 9

Calls

3 calls:

200.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
125.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
273.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	358	751
1	1116	706
2	5002	701

prune227.0ms

Filtered

80 candidates to 53 candidates (66.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	80	9	89

Merged error: 2.8b

Counts

89 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

14.5b	(cbrt (* K (+ m n)))
14.5b	(cbrt (* K (+ m n)))
14.5b	(cbrt (* K (+ m n)))
33.3b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
19×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`associate-r`
9×	`associate-l`
6×	`cbrt-div` `associate-*r/`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 79

Calls

4 calls:

6.0ms	(cbrt (* K (+ m n)))
6.0ms	(cbrt (* K (+ m n)))
6.0ms	(cbrt (* K (+ m n)))
180.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series401.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (* K (+ m n)))
110.0ms	(cbrt (* K (+ m n)))
111.0ms	(cbrt (* K (+ m n)))
65.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify98.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 4 (89.0ms)

Iter	Nodes	Cost
0	228	730
1	532	680
2	1345	656
3	3543	647
4	5001	641

prune439.0ms

Filtered

91 candidates to 73 candidates (80.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	84	7	91
Fresh	5	2	7
Picked	1	0	1
Done	0	1	1
Total	90	10	100

Merged error: 2.7b

Counts

100 → 10

localize32.0ms

Local error

Found 4 expressions with local error:

14.5b	(cbrt (* K (+ m n)))
14.5b	(cbrt (* K (+ m n)))
14.5b	(cbrt (* K (+ m n)))
33.3b	(cos (- (/ (* (* (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n))))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
19×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`associate-r`
9×	`associate-l`
6×	`cbrt-div` `associate-*r/`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 79

Calls

4 calls:

6.0ms	(cbrt (* K (+ m n)))
11.0ms	(cbrt (* K (+ m n)))
6.0ms	(cbrt (* K (+ m n)))
1.8s	(cos (- (/ (* (* (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n))))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series377.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(cbrt (* K (+ m n)))
106.0ms	(cbrt (* K (+ m n)))
109.0ms	(cbrt (* K (+ m n)))
56.0ms	(cos (- (/ (* (* (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n))))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify108.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 4 (98.0ms)

Iter	Nodes	Cost
0	237	906
1	565	834
2	1463	810
3	4086	801
4	5002	795

prune436.0ms

Filtered

91 candidates to 73 candidates (80.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	85	6	91
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	89	12	101

Merged error: 2.7b

Counts

101 → 12

regimes429.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	23	10
2	23	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

684.0ms	8068×	body	80	valid
61.0ms	119×	body	1280	valid
56.0ms	158×	body	640	valid
25.0ms	97×	body	320	valid
11.0ms	43×	body	160	valid
2.0ms	3×	body	2560	valid