Details

sample46.0ms

Algorithm

intervals

Results

20.0ms	266×	body	80	valid
4.0ms	12×	body	640	valid
1.0ms	3×	body	1280	valid
1.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify53.0ms

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.0b

localize23.0ms

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)
31.3b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.2s

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:

19.0ms	(* K (+ m n))
1.1s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
55.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
38.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series557.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* K (+ m n))
194.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
270.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
65.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify102.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 2 (66.0ms)

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

prune689.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- l (fabs (- 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)

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

189×	`add-sqr-sqrt`
158×	`*-un-lft-identity`
138×	`prod-diff`
78×	`unpow-prod-down`
72×	`add-cube-cbrt`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
52×	`difference-of-squares`
44×	`distribute-lft-out--`
27×	`fma-neg`
15×	`add-log-exp`
13×	`times-frac` `sqr-pow`
11×	`associate--r+`
7×	`diff-log`
6×	`neg-mul-1`
4×	`pow1` `add-exp-log`
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 → 229

Calls

3 calls:

6.0ms	(- l (fabs (- m n)))
1.1s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
55.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series472.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(- l (fabs (- m n)))
194.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
264.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify84.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	650	5353
1	1866	3800
2	5001	3192

prune447.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.5b

localize43.0ms

Local error

Found 4 expressions with local error:

11.6b	(cbrt (/ (* K (+ m n)) 2.0))
11.6b	(cbrt (/ (* K (+ m n)) 2.0))
31.2b	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))
31.3b	(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-div` `pow1/3` `fma-udef` `div-inv`
1×	`cos-sum` `sin-sum`

Counts

4 → 56

Calls

4 calls:

6.0ms	(cbrt (/ (* K (+ m n)) 2.0))
6.0ms	(cbrt (/ (* K (+ m n)) 2.0))
5.0ms	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))
3.0ms	(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))

series1.6s

Counts

4 → 12

Calls

4 calls:

165.0ms	(cbrt (/ (* K (+ m n)) 2.0))
165.0ms	(cbrt (/ (* K (+ m n)) 2.0))
532.0ms	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))
716.0ms	(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))

simplify58.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	270	940
1	622	851
2	1689	835
3	5002	831

prune669.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.5b

localize49.0ms

Local error

Found 4 expressions with local error:

11.6b	(cbrt (/ (* K (+ m n)) 2.0))
11.6b	(cbrt (/ (* K (+ m n)) 2.0))
31.2b	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))
31.3b	(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-div` `pow1/3` `fma-udef` `div-inv`
1×	`cos-sum` `sin-sum`

Counts

4 → 56

Calls

4 calls:

6.0ms	(cbrt (/ (* K (+ m n)) 2.0))
6.0ms	(cbrt (/ (* K (+ m n)) 2.0))
2.0ms	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))
3.0ms	(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))

series1.4s

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt (/ (* K (+ m n)) 2.0))
161.0ms	(cbrt (/ (* K (+ m n)) 2.0))
541.0ms	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))
522.0ms	(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))

simplify58.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	270	940
1	622	851
2	1689	835
3	5002	831

prune701.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.5b

regimes367.0ms

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

622.0ms	8115×	body	80	valid
53.0ms	165×	body	640	valid
51.0ms	113×	body	1280	valid
24.0ms	106×	body	320	valid
9.0ms	57×	body	160	valid
4.0ms	5×	body	2560	valid