Details

sample46.0ms

Algorithm

intervals

Results

24.0ms	261×	body	80	valid
2.0ms	5×	body	640	valid
2.0ms	3×	body	1280	valid
1.0ms	1×	body	2560	valid
1.0ms	3×	body	160	valid

simplify48.0ms

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: 12.5b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
32.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms	(* K (+ m n))
16.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series552.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
24.0ms	(* K (+ m n))
191.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
54.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify55.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	411	566
1	1369	528
2	5001	523

prune272.0ms

Filtered

82 candidates to 58 candidates (70.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 1.3b

Counts

83 → 5

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- 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))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 78

Calls

3 calls:

21.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
16.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

series585.0ms

Counts

3 → 9

Calls

3 calls:

155.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
258.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
172.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

simplify48.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	412	1003
1	1570	932
2	5002	908

prune199.0ms

Filtered

87 candidates to 54 candidates (62.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	87	5	92

Merged error: 1.3b

Counts

92 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- (/ (+ m n) 2.0) M))
0.6b	(pow (cbrt (- (/ (+ m n) 2.0) M)) 2.0)
0.6b	(* (cbrt (- (/ (+ m n) 2.0) M)) (cbrt (- (/ (+ m n) 2.0) M)))
32.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
44×	`cbrt-prod`
34×	`*-un-lft-identity`
16×	`add-cube-cbrt`
14×	`cbrt-div`
12×	`pow1` `difference-of-squares`
11×	`swap-sqr`
9×	`unpow-prod-down` `associate-r` `associate-l`
8×	`pow1/3` `distribute-lft-out--`
7×	`add-exp-log` `flip3--` `flip--`
6×	`times-frac`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`pow-unpow`
2×	`cos-sum` `pow-pow` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `cos-diff` `pow-to-exp` `sub-neg` `pow-plus` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 109

Calls

4 calls:

8.0ms	(cbrt (- (/ (+ m n) 2.0) M))
10.0ms	(pow (cbrt (- (/ (+ m n) 2.0) M)) 2.0)
24.0ms	(* (cbrt (- (/ (+ m n) 2.0) M)) (cbrt (- (/ (+ m n) 2.0) M)))
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series843.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(cbrt (- (/ (+ m n) 2.0) M))
303.0ms	(pow (cbrt (- (/ (+ m n) 2.0) M)) 2.0)
232.0ms	(* (cbrt (- (/ (+ m n) 2.0) M)) (cbrt (- (/ (+ m n) 2.0) M)))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify53.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	493	1304
1	1730	1199
2	5002	1144

prune524.0ms

Filtered

121 candidates to 86 candidates (71.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	121	5	126

Merged error: 1.3b

Counts

126 → 5

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- (/ (+ m n) 2.0) M))
0.6b	(pow (cbrt (- (/ (+ m n) 2.0) M)) 2.0)
0.9b	(pow (cbrt (cbrt (- (/ (+ m n) 2.0) M))) 4)
32.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod` `add-sqr-sqrt`
21×	`unpow-prod-down`
18×	`*-un-lft-identity`
12×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `pow-unpow` `difference-of-squares`
4×	`pow-pow` `add-cbrt-cube` `add-log-exp`
3×	`times-frac` `pow1/3` `distribute-lft-out--`
2×	`pow-to-exp` `cbrt-div` `cos-sum` `pow-exp` `sqr-pow`
1×	`cos-diff` `sub-neg` `flip3--` `flip--`

Counts

4 → 77

Calls

4 calls:

8.0ms	(cbrt (- (/ (+ m n) 2.0) M))
10.0ms	(pow (cbrt (- (/ (+ m n) 2.0) M)) 2.0)
11.0ms	(pow (cbrt (cbrt (- (/ (+ m n) 2.0) M))) 4)
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.2s

Counts

4 → 12

Calls

4 calls:

285.0ms	(cbrt (- (/ (+ m n) 2.0) M))
300.0ms	(pow (cbrt (- (/ (+ m n) 2.0) M)) 2.0)
534.0ms	(pow (cbrt (cbrt (- (/ (+ m n) 2.0) M))) 4)
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	518	829
1	1539	785
2	5001	760

prune457.0ms

Filtered

89 candidates to 68 candidates (76.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	89	5	94

Merged error: 1.3b

Counts

94 → 5

regimes184.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

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

790.0ms	8093×	body	80	valid
67.0ms	112×	body	1280	valid
65.0ms	155×	body	640	valid
32.0ms	110×	body	320	valid
13.0ms	66×	body	160	valid
2.0ms	2×	body	2560	valid

Details

sample46.0ms

simplify48.0ms

prune9.0ms

localize25.0ms

rewrite41.0ms

series552.0ms

simplify55.0ms

prune272.0ms

localize14.0ms

rewrite49.0ms

series585.0ms

simplify48.0ms

prune199.0ms

localize27.0ms

rewrite54.0ms

series843.0ms

simplify53.0ms

prune524.0ms

localize37.0ms

rewrite40.0ms

series1.2s

simplify46.0ms

prune457.0ms

regimes184.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling