Details

sample67.0ms

Algorithm

intervals

Results

44.0ms	258×	body	80	valid
3.0ms	4×	body	1280	valid
3.0ms	5×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify50.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

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)
34.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite731.0ms

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:

10.0ms	(* K (+ m n))
652.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
34.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series517.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* K (+ m n))
178.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
259.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
53.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify107.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 2 (65.0ms)

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

prune685.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

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)

rewrite695.0ms

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:

650.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
30.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series439.0ms

Counts

2 → 6

Calls

2 calls:

179.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
259.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify73.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (41.0ms)

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

prune380.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize40.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
33.7b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
34.0b	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `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`
2×	`pow1/3` `fma-udef`
1×	`cos-sum` `sin-sum`

Counts

4 → 46

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
1.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
1.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

series415.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
204.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
210.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify130.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (27.0ms)

Iter	Nodes	Cost
0	162	538
1	381	481
2	991	472
3	3226	466
4	5001	466

prune470.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize48.0ms

Local error

Found 4 expressions with local error:

33.7b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
33.7b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
33.7b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
34.0b	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`
3×	`cos-sum`
1×	`sin-sum`

Counts

4 → 40

Calls

4 calls:

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

series845.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
209.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
209.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
217.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify59.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	108	754
1	251	653
2	596	652
3	1348	652
4	5002	652

prune505.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.3b

regimes268.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

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

sample2.0s

Algorithm

intervals

Results

1.4s	8116×	body	80	valid
99.0ms	124×	body	1280	valid
95.0ms	162×	body	640	valid
41.0ms	93×	body	320	valid
21.0ms	66×	body	160	valid