Details

sample58.0ms

Algorithm

intervals

Results

34.0ms	258×	body	80	valid
4.0ms	7×	body	640	valid
2.0ms	5×	body	320	valid
1.0ms	1×	body	1280	valid
0.0ms	1×	body	160	valid

simplify51.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.5b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite751.0ms

Algorithm

rewrite-expression-head

Rules

198×	`add-sqr-sqrt`
167×	`*-un-lft-identity`
150×	`prod-diff`
81×	`add-cube-cbrt`
78×	`unpow-prod-down`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
51×	`difference-of-squares`
43×	`distribute-lft-out--`
24×	`fma-neg`
23×	`cos-sum`
22×	`times-frac`
14×	`add-log-exp`
13×	`sqr-pow`
11×	`associate--r+`
7×	`pow1` `add-exp-log`
6×	`neg-mul-1` `diff-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`sub-neg` `pow-unpow` `associate-l` `div-inv`
2×	`associate-*r/` `neg-log`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr`

Counts

4 → 259

Calls

4 calls:

9.0ms	(* K (+ m n))
669.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
35.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series509.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* K (+ m n))
175.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
254.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify106.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	991	6064
1	2883	4404
2	5001	4329

prune708.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.5b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite719.0ms

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:

670.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
34.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series475.0ms

Counts

2 → 6

Calls

2 calls:

193.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
282.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (43.0ms)

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

prune383.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
33.2b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

0.0ms	(cbrt K)
0.0ms	(cbrt K)
1.0ms	(cbrt K)
54.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series617.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt K)
170.0ms	(cbrt K)
178.0ms	(cbrt K)
96.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify81.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	356	1441
1	740	1183
2	2530	1177
3	5002	1054

prune399.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
33.2b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
33.2b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
33.2b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite171.0ms

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:

1.0ms	(cbrt K)
52.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
52.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
61.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series570.0ms

Counts

4 → 12

Calls

4 calls:

279.0ms	(cbrt K)
99.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
95.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
97.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify95.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	356	3979
1	740	3229
2	2530	3227
3	5002	2866

prune493.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.5b

regimes362.0ms

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	21	10
1	23	10
2	23	10

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.1s	8081×	body	80	valid
95.0ms	177×	body	640	valid
80.0ms	112×	body	1280	valid
44.0ms	108×	body	320	valid
14.0ms	49×	body	160	valid
2.0ms	2×	body	2560	valid