Details

sample51.0ms

Algorithm

intervals

Results

26.0ms	259×	body	80	valid
3.0ms	6×	body	1280	valid
2.0ms	4×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify54.0ms

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: 14.7b

Counts

2 → 1

localize23.0ms

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

rewrite40.0ms

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:

9.0ms	(- (/ (* K (+ m n)) 2.0) M)
6.0ms	(* K (+ m n))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
11.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series404.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (/ (* K (+ m n)) 2.0) M)
25.0ms	(* K (+ m n))
265.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify64.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (48.0ms)

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

prune412.0ms

Filtered

136 candidates to 82 candidates (60.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	131	5	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	5	137

Merged error: 1.1b

Counts

137 → 5

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

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:

10.0ms

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

series264.0ms

Counts

1 → 3

Calls

1 calls:

264.0ms

(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

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	25	5	30

Merged error: 1.1b

Counts

30 → 5

localize24.0ms

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))
0.4b	(/ (+ m n) (sqrt 2.0))
33.1b	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

rewrite16.0ms

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:

1.0ms	(fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M))
4.0ms	(/ K (sqrt 2.0))
6.0ms	(/ (+ m n) (sqrt 2.0))
2.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

series579.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M))
52.0ms	(/ K (sqrt 2.0))
91.0ms	(/ (+ m n) (sqrt 2.0))
213.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

simplify95.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	301	846
1	906	777
2	3539	748
3	5001	739

prune438.0ms

Filtered

123 candidates to 81 candidates (65.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	123	5	128

Merged error: 1.1b

Counts

128 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ K (sqrt 2.0))
0.4b	(/ (+ m n) (sqrt 2.0))
0.7b	(log (exp (cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))))
33.1b	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
42×	`times-frac`
38×	`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*`
5×	`pow1`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod`
2×	`cbrt-undiv` `cos-sum` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv` `associate-/l/`
1×	`log-div` `flip3-+` `exp-diff` `rem-log-exp` `flip-+`

Counts

4 → 119

Calls

4 calls:

4.0ms	(/ K (sqrt 2.0))
6.0ms	(/ (+ m n) (sqrt 2.0))
3.0ms	(log (exp (cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))))
2.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

series567.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ K (sqrt 2.0))
95.0ms	(/ (+ m n) (sqrt 2.0))
203.0ms	(log (exp (cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))))
207.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

simplify56.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	305	957
1	792	887
2	1994	865
3	5001	865

prune475.0ms

Filtered

131 candidates to 86 candidates (65.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	131	5	136

Merged error: 1.1b

Counts

136 → 5

regimes181.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

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

799.0ms	8097×	body	80	valid
69.0ms	161×	body	640	valid
67.0ms	117×	body	1280	valid
33.0ms	100×	body	320	valid
13.0ms	63×	body	160	valid
4.0ms	5×	body	2560	valid

Details

sample51.0ms

simplify54.0ms

prune14.0ms

localize23.0ms

rewrite40.0ms

series404.0ms

simplify64.0ms

prune412.0ms

localize14.0ms

rewrite11.0ms

series264.0ms

simplify46.0ms

prune91.0ms

localize24.0ms

rewrite16.0ms

series579.0ms

simplify95.0ms

prune438.0ms

localize28.0ms

rewrite18.0ms

series567.0ms

simplify56.0ms

prune475.0ms

regimes181.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling