Details

sample45.0ms

Algorithm

intervals

Results

19.0ms	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

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	50	16
1	93	16
2	200	16
3	517	15
4	1893	15
5	5001	15

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.8b

localize28.0ms

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))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `unpow-prod-down`
5×	`add-cbrt-cube`
4×	`associate-r`
3×	`pow-unpow` `associate-l` `add-log-exp`
2×	`cos-sum` `associate-*r/` `difference-of-squares`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr` `sqr-pow`

Counts

3 → 53

Calls

3 calls:

19.0ms	(* K (+ m n))
58.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
28.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series327.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(* K (+ m n))
251.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify98.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	318	362
1	1070	336
2	4261	335
3	5003	332

prune271.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.3b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite57.0ms

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×	`pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 20

Calls

1 calls:

56.0ms

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

series249.0ms

Counts

1 → 3

Calls

1 calls:

249.0ms

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

simplify44.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	156	164
1	433	159
2	1446	158
3	5001	155

prune104.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.3b

localize20.0ms

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))

rewrite532.0ms

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×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 129

Calls

4 calls:

382.0ms	(* (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)) (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)))
47.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
47.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
50.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

287.0ms	(* (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)) (cbrt (pow (- (/ (+ m n) 2.0) M) 2.0)))
292.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
289.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
284.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))

simplify89.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	327	1856
1	973	1773
2	3361	1657
3	5003	1638

prune825.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.3b

localize30.0ms

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))

rewrite193.0ms

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` `times-frac` `pow1/3` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

48.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
48.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
49.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
46.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

289.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
285.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
288.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))
281.0ms	(cbrt (pow (- (/ (+ m n) 2.0) M) 2.0))

simplify128.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 4 (118.0ms)

Iter	Nodes	Cost
0	175	848
1	374	800
2	1059	788
3	4152	764
4	5001	756

prune487.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.3b

regimes198.0ms

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

619.0ms	8100×	body	80	valid
62.0ms	128×	body	1280	valid
47.0ms	144×	body	640	valid
27.0ms	106×	body	320	valid
9.0ms	60×	body	160	valid
1.0ms	1×	body	2560	valid