Details

sample43.0ms

Algorithm

intervals

Results

19.0ms	260×	body	80	valid
2.0ms	5×	body	1280	valid
2.0ms	6×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	15
5	5001	15

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(* K (+ m n))
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

208×	`add-sqr-sqrt`
180×	`*-un-lft-identity`
171×	`prod-diff`
94×	`add-cube-cbrt`
72×	`unpow-prod-down`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
50×	`difference-of-squares`
43×	`distribute-lft-out--`
33×	`times-frac`
31×	`fma-neg`
23×	`cos-sum`
16×	`add-log-exp`
12×	`sqr-pow`
11×	`associate--r+`
7×	`diff-log` `div-inv`
6×	`pow1` `add-exp-log` `neg-mul-1` `add-cbrt-cube`
4×	`expm1-log1p-u` `sub-neg` `associate-r` `log1p-expm1-u`
3×	`associate-l`
2×	`flip3--` `associate-*r/` `neg-log` `flip--`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr`

Counts

4 → 281

Calls

4 calls:

1.1s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
23.0ms	(- (/ (* K (+ m n)) 2.0) M)
19.0ms	(* K (+ m n))
35.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series340.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
58.0ms	(- (/ (* K (+ m n)) 2.0) M)
32.0ms	(* K (+ m n))
61.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify109.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	984	6370
1	2848	4545
2	5002	4468

prune738.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.2b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
148×	`*-un-lft-identity`
129×	`prod-diff`
78×	`unpow-prod-down`
64×	`add-cube-cbrt`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
51×	`difference-of-squares`
43×	`distribute-lft-out--`
24×	`fma-neg`
13×	`times-frac` `sqr-pow`
12×	`add-log-exp`
11×	`associate--r+`
6×	`neg-mul-1` `diff-log`
3×	`pow1` `add-exp-log` `pow-unpow`
2×	`expm1-log1p-u` `sub-neg` `neg-log` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `flip--` `associate--r-`

Counts

2 → 201

Calls

2 calls:

55.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.1s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series471.0ms

Counts

2 → 6

Calls

2 calls:

276.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
194.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify70.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	608	5050
1	1693	3609
2	5001	3001

prune542.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.2b

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
34.2b	(cos (+ (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M) (fma (- M) 1 M)))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-diff` `associate-+l-` `cos-sum`

Counts

4 → 50

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
287.0ms	(cos (+ (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M) (fma (- M) 1 M)))

series220.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
220.0ms	(cos (+ (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M) (fma (- M) 1 M)))

simplify55.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 4 (50.0ms)

Iter	Nodes	Cost
0	148	424
1	331	388
2	839	382
3	2139	379
4	5001	357

prune364.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
34.2b	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`cos-sum`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `prod-diff`
1×	`cos-diff` `sub-neg`

Counts

4 → 54

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
68.0ms	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

series206.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
206.0ms	(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

simplify61.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 4 (51.0ms)

Iter	Nodes	Cost
0	180	484
1	364	448
2	844	442
3	2059	436
4	5002	421

prune333.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.2b

regimes202.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	23	10
2	23	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

610.0ms	8092×	body	80	valid
59.0ms	125×	body	1280	valid
41.0ms	129×	body	640	valid
24.0ms	92×	body	320	valid
12.0ms	55×	body	160	valid
1.0ms	2×	body	2560	valid