Details

sample38.0ms

Algorithm

intervals

Results

20.0ms	260×	body	80	valid
1.0ms	4×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	1280	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: 14.5b

localize26.0ms

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))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
34.7b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite742.0ms

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:

662.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
12.0ms	(* K (+ m n))
31.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series525.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
31.0ms	(* K (+ m n))
258.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify103.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 2 (63.0ms)

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

prune699.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize20.0ms

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)

rewrite707.0ms

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:

663.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
31.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series447.0ms

Counts

2 → 6

Calls

2 calls:

183.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
263.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify79.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (42.0ms)

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

prune369.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize46.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
34.7b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
34.7b	(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))))

series414.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
205.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
209.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify128.0ms

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

prune449.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (fma K n (* m K)) 3)
1.3b	(fma K n (* m K))
25.8b	(cbrt (pow (fma K n (* m K)) 3))
34.7b	(cos (- (/ (cbrt (pow (fma K n (* m K)) 3)) 2.0) M))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

149×	`cos-sum`
147×	`prod-diff`
143×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
135×	`times-frac`
120×	`cbrt-prod`
33×	`unpow-prod-down` `cube-prod`
11×	`cube-mult` `unpow3` `sqr-pow`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `div-inv`
1×	`cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

4 → 217

Calls

4 calls:

1.0ms	(pow (fma K n (* m K)) 3)
0.0ms	(fma K n (* m K))
1.0ms	(cbrt (pow (fma K n (* m K)) 3))
89.0ms	(cos (- (/ (cbrt (pow (fma K n (* m K)) 3)) 2.0) M))

series179.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(pow (fma K n (* m K)) 3)
32.0ms	(fma K n (* m K))
38.0ms	(cbrt (pow (fma K n (* m K)) 3))
52.0ms	(cos (- (/ (cbrt (pow (fma K n (* m K)) 3)) 2.0) M))

simplify106.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	1319	7694
1	2395	6106
2	5002	5814

prune430.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.6b

regimes151.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.2b 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

sample1.0s

Algorithm

intervals

Results

628.0ms	8103×	body	80	valid
51.0ms	158×	body	640	valid
49.0ms	106×	body	1280	valid
24.0ms	104×	body	320	valid
7.0ms	46×	body	160	valid
3.0ms	4×	body	2560	valid