Details

sample50.0ms

Algorithm

intervals

Results

25.0ms	259×	body	80	valid
4.0ms	6×	body	1280	valid
2.0ms	6×	body	640	valid
1.0ms	4×	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	95	16
2	211	16
3	553	15
4	1974	15
5	5001	15

prune14.0ms

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: 16.9b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
35.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

10.0ms	(- (/ (* K (+ m n)) 2.0) M)
6.0ms	(* K (+ m n))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
12.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series397.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (/ (* K (+ m n)) 2.0) M)
25.0ms	(* K (+ m n))
256.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify67.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	612	1660
1	1907	1270
2	5003	1268

prune448.0ms

Filtered

136 candidates to 82 candidates (60.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	4	137

Merged error: 1.2b

Counts

137 → 4

localize15.0ms

Local error

Found 2 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)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
13×	`times-frac`
6×	`unpow-prod-down` `pow-flip`
5×	`exp-prod`
4×	`pow1` `add-exp-log` `exp-sum` `associate-/r*` `add-cbrt-cube`
3×	`pow-unpow` `associate-/l*`
2×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `distribute-lft-out` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
1×	`cbrt-undiv` `pow-to-exp` `associate-+r-` `rec-exp` `pow-pow` `frac-2neg` `exp-diff` `1-exp` `pow-exp` `clear-num` `associate-/r/` `div-inv` `inv-pow` `sqr-pow`

Counts

2 → 65

Calls

2 calls:

22.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
12.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series429.0ms

Counts

2 → 6

Calls

2 calls:

167.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
262.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	362	833
1	1322	765
2	5001	744

prune203.0ms

Filtered

71 candidates to 45 candidates (63.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	71	4	75

Merged error: 1.2b

Counts

75 → 4

localize20.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`add-cube-cbrt` `pow-unpow`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 22

Calls

1 calls:

11.0ms

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

series271.0ms

Counts

1 → 3

Calls

1 calls:

271.0ms

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

simplify46.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	159	174
1	445	168
2	1492	167
3	5001	162

prune91.0ms

Filtered

25 candidates to 19 candidates (76.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	25	4	29

Merged error: 1.2b

Counts

29 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M))
0.4b	(/ K (sqrt 2.0))
0.5b	(/ (+ m n) (sqrt 2.0))
35.8b	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
42×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`sqrt-prod`
12×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out` `associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv` `associate-/l/`
1×	`cos-sum` `flip3-+` `flip-+`

Counts

4 → 111

Calls

4 calls:

4.0ms	(fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M))
4.0ms	(/ K (sqrt 2.0))
7.0ms	(/ (+ m n) (sqrt 2.0))
2.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

series589.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M))
57.0ms	(/ K (sqrt 2.0))
88.0ms	(/ (+ m n) (sqrt 2.0))
210.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

simplify100.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	301	846
1	906	777
2	3539	766
3	5001	757

prune487.0ms

Filtered

123 candidates to 90 candidates (73.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	122	5	127

Merged error: 1.2b

Counts

127 → 5

regimes191.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.0b and baseline of 1.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	23	10
2	23	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

801.0ms	8111×	body	80	valid
69.0ms	109×	body	1280	valid
68.0ms	164×	body	640	valid
30.0ms	99×	body	320	valid
12.0ms	59×	body	160	valid
2.0ms	3×	body	2560	valid