Details

sample48.0ms

Algorithm

intervals

Results

26.0ms	264×	body	80	valid
2.0ms	4×	body	1280	valid
1.0ms	3×	body	640	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	320	valid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	15
5	5002	15

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 14.3b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
32.9b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 380

Calls

4 calls:

6.0ms	(* K (+ m n))
28.0ms	(- (/ (* K (+ m n)) 2.0) M)
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
43.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series450.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* K (+ m n))
65.0ms	(- (/ (* K (+ m n)) 2.0) M)
298.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
60.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify147.0ms

Algorithm

egg-herbie

Counts

392 → 392

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	1485	8354
1	3582	6416
2	5002	6323

prune840.0ms

Filtered

392 candidates to 157 candidates (59.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	387	5	392
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	388	5	393

Merged error: 1.1b

Counts

393 → 5

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

233×	`add-sqr-sqrt`
223×	`*-un-lft-identity`
177×	`prod-diff`
113×	`add-cube-cbrt`
78×	`unpow-prod-down`
62×	`distribute-rgt-neg-in` `times-frac`
60×	`distribute-lft-neg-in`
53×	`difference-of-squares`
44×	`distribute-lft-out--`
40×	`fma-neg`
15×	`add-log-exp`
13×	`sqr-pow`
12×	`distribute-lft-out`
11×	`associate--r+`
7×	`diff-log`
6×	`neg-mul-1`
4×	`pow1` `add-exp-log` `div-inv`
3×	`expm1-log1p-u` `sub-neg` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `neg-log` `flip--`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `pow-exp` `associate--r-`

Counts

3 → 282

Calls

3 calls:

17.0ms	(- (/ (+ m n) 2.0) M)
26.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series532.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(- (/ (+ m n) 2.0) M)
208.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
294.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify114.0ms

Algorithm

egg-herbie

Counts

291 → 291

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	812	5976
1	2453	4207
2	5001	4117

prune478.0ms

Filtered

291 candidates to 115 candidates (60.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	291	0	291
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	291	5	296

Merged error: 1.1b

Counts

296 → 5

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (/ 1 (sqrt 2.0)) (/ (* K (+ m n)) (sqrt 2.0)) (- M))
0.4b	(/ (* K (+ m n)) (sqrt 2.0))
1.0b	(/ 1 (sqrt 2.0))
33.0b	(cos (fma (/ 1 (sqrt 2.0)) (/ (* K (+ m n)) (sqrt 2.0)) (- M)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
82×	`add-sqr-sqrt` `*-un-lft-identity`
68×	`add-cube-cbrt`
54×	`sqrt-prod`
28×	`associate-r`
21×	`associate-l`
16×	`associate-/l*`
13×	`add-exp-log`
12×	`associate-/r*`
11×	`add-cbrt-cube`
7×	`*-commutative` `distribute-lft-out` `unswap-sqr`
6×	`pow1`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-flip`
2×	`frac-2neg` `associate-*r/` `clear-num` `fma-udef` `div-inv` `associate-/l/`
1×	`rec-exp` `cos-sum` `sqrt-pow1` `flip3-+` `pow1/2` `1-exp` `prod-exp` `cbrt-unprod` `flip-+` `inv-pow`

Counts

4 → 182

Calls

4 calls:

1.0ms	(fma (/ 1 (sqrt 2.0)) (/ (* K (+ m n)) (sqrt 2.0)) (- M))
12.0ms	(/ (* K (+ m n)) (sqrt 2.0))
5.0ms	(/ 1 (sqrt 2.0))
2.0ms	(cos (fma (/ 1 (sqrt 2.0)) (/ (* K (+ m n)) (sqrt 2.0)) (- M)))

series627.0ms

Counts

4 → 10

Calls

4 calls:

258.0ms	(fma (/ 1 (sqrt 2.0)) (/ (* K (+ m n)) (sqrt 2.0)) (- M))
117.0ms	(/ (* K (+ m n)) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))
252.0ms	(cos (fma (/ 1 (sqrt 2.0)) (/ (* K (+ m n)) (sqrt 2.0)) (- M)))

simplify77.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	551	1511
1	2538	1372
2	5001	1337

prune613.0ms

Filtered

192 candidates to 112 candidates (41.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	192	5	197

Merged error: 1.1b

Counts

197 → 5

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
32.9b	(cos (- (/ (* K (+ m n)) 2.0) M))
32.9b	(cos (- (/ (* K (+ m n)) 2.0) M))
32.9b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

395×	`add-sqr-sqrt` `*-un-lft-identity`
393×	`cos-sum`
387×	`prod-diff`
351×	`times-frac`
341×	`add-cube-cbrt`
108×	`associate-r`
81×	`associate-l`
27×	`*-commutative` `distribute-lft-out` `unswap-sqr`
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 → 436

Calls

4 calls:

8.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
39.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
43.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
39.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series337.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
60.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
65.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify174.0ms

Algorithm

egg-herbie

Counts

448 → 448

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	1219	16804
1	2204	13572
2	5001	12904

prune946.0ms

Filtered

448 candidates to 101 candidates (77.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	444	4	448
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	445	8	453

Merged error: 1.1b

Counts

453 → 8

regimes366.0ms

Accuracy

0% (0.3b remaining)

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

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

sample1.2s

Algorithm

intervals

Results

737.0ms	8116×	body	80	valid
59.0ms	154×	body	640	valid
55.0ms	101×	body	1280	valid
28.0ms	101×	body	320	valid
11.0ms	52×	body	160	valid
2.0ms	2×	body	2560	valid