Details

sample47.0ms

Algorithm

intervals

Results

25.0ms	261×	body	80	valid
2.0ms	4×	body	1280	valid
1.0ms	2×	body	640	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	320	valid

simplify50.0ms

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

prune10.0ms

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: 17.3b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

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) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
38.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

17.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
18.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
6.0ms	(* K (+ m n))
11.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series377.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
177.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
24.0ms	(* K (+ m n))
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify67.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	678	1591
1	2088	1291
2	5003	1283

prune424.0ms

Filtered

127 candidates to 85 candidates (66.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	4	128

Merged error: 1.2b

Counts

128 → 4

localize18.0ms

Local error

Found 2 expressions with local error:

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) (- l (fabs (- m n))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 57

Calls

2 calls:

17.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
18.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

series287.0ms

Counts

2 → 6

Calls

2 calls:

112.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
175.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))

simplify36.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	291	577
1	932	496
2	5001	475

prune207.0ms

Filtered

63 candidates to 47 candidates (74.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	63	4	67

Merged error: 1.2b

Counts

67 → 4

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
38.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
38.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
38.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cos-sum`
63×	`prod-diff`
44×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`div-inv`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 112

Calls

4 calls:

2.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
12.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
12.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
12.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series307.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
51.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify90.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 4 (69.0ms)

Iter	Nodes	Cost
0	313	2908
1	519	2268
2	1140	2266
3	3283	2085
4	5002	2049

prune367.0ms

Filtered

124 candidates to 58 candidates (46.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	123	5	128

Merged error: 1.2b

Counts

128 → 5

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
38.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
38.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
38.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cos-sum`
63×	`prod-diff`
44×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`div-inv`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 112

Calls

4 calls:

2.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
15.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
11.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
11.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series294.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
50.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
51.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify90.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 4 (66.0ms)

Iter	Nodes	Cost
0	313	2908
1	519	2268
2	1140	2266
3	3283	2085
4	5002	2049

prune372.0ms

Filtered

124 candidates to 58 candidates (46.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	124	5	129

Merged error: 1.2b

Counts

129 → 5

regimes229.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

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

812.0ms	8136×	body	80	valid
73.0ms	121×	body	1280	valid
58.0ms	140×	body	640	valid
32.0ms	103×	body	320	valid
11.0ms	52×	body	160	valid
3.0ms	3×	body	2560	valid