Details

sample43.0ms

Algorithm

intervals

Results

18.0ms	253×	body	80	valid
2.0ms	5×	body	1280	valid
2.0ms	7×	body	320	valid
1.0ms	3×	body	640	valid
0.0ms	1×	body	160	valid

simplify50.0ms

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.8b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`cos-sum`
21×	`prod-diff`
20×	`add-cube-cbrt`
10×	`times-frac`
6×	`pow1` `add-exp-log` `unpow-prod-down`
5×	`add-cbrt-cube`
4×	`associate-r`
3×	`expm1-log1p-u` `pow-unpow` `associate-l` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`associate-*r/` `difference-of-squares`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `flip3-+` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr` `sqr-pow`

Counts

3 → 80

Calls

3 calls:

18.0ms	(* K (+ m n))
54.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
34.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series340.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(* K (+ m n))
256.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
59.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify51.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	547	1188
1	1611	963
2	5002	962

prune322.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.3b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`add-cube-cbrt` `pow-unpow`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 22

Calls

1 calls:

56.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

series263.0ms

Counts

1 → 3

Calls

1 calls:

263.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	159	174
1	445	168
2	1492	167
3	5001	162

prune102.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)) (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)))
37.8b	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
37.8b	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
37.8b	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))

rewrite519.0ms

Algorithm

rewrite-expression-head

Rules

98×	`cbrt-prod`
81×	`add-sqr-sqrt`
54×	`unpow-prod-down`
42×	`*-un-lft-identity`
22×	`add-cube-cbrt`
16×	`unswap-sqr`
15×	`swap-sqr` `sqr-pow`
14×	`difference-of-squares`
13×	`associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `distribute-lft-out--`
7×	`times-frac`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 137

Calls

4 calls:

374.0ms	(* (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)) (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)))
46.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
46.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
47.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

309.0ms	(* (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)) (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)))
308.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
306.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
303.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))

simplify86.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	331	1916
1	995	1833
2	3474	1717
3	5001	1690

prune645.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.3b

localize23.0ms

Local error

Found 4 expressions with local error:

37.8b	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
37.8b	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
37.8b	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
37.8b	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

40×	`cbrt-prod`
32×	`add-sqr-sqrt`
24×	`unpow-prod-down`
20×	`*-un-lft-identity`
12×	`add-cube-cbrt`
8×	`difference-of-squares`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `times-frac` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

46.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
46.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
46.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
48.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

322.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
319.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
310.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
316.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))

simplify139.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	177	896
1	384	848
2	1114	836
3	4362	804
4	5001	804

prune510.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.3b

regimes195.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	63
1	57	63
2	59	63
3	59	63

end0.0ms

sample1.2s

Algorithm

intervals

Results

643.0ms	8100×	body	80	valid
62.0ms	128×	body	1280	valid
48.0ms	144×	body	640	valid
26.0ms	106×	body	320	valid
10.0ms	60×	body	160	valid
1.0ms	1×	body	2560	valid