Details

sample39.0ms

Algorithm

intervals

Results

21.0ms	260×	body	80	valid
1.0ms	10×	body	80	overflowed
1.0ms	1×	body	1280	valid
0.0ms	1×	body	640	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite61.0ms

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:

13.0ms	(* K (+ m n))
32.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
15.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series345.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* K (+ m n))
266.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
54.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify102.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (97.0ms)

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

prune260.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite35.0ms

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:

35.0ms

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

series268.0ms

Counts

1 → 3

Calls

1 calls:

268.0ms

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

simplify46.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 3 (43.0ms)

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

prune88.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (* K (+ m n))) (sqrt (* K (+ m n))))
8.5b	(sqrt (* K (+ m n)))
8.5b	(sqrt (* K (+ m n)))
15.0b	(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

59×	`pow1`
32×	`sqrt-pow1`
22×	`pow-prod-down`
18×	`associate-*r/`
16×	`sqrt-div`
12×	`pow1/2`
10×	`add-sqr-sqrt` `pow-prod-up`
8×	`add-cube-cbrt` `*-un-lft-identity` `flip3-+` `flip-+`
6×	`add-exp-log` `sqrt-prod` `pow-sqr` `add-cbrt-cube`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `add-log-exp`
2×	`cos-sum` `associate-*l/`
1×	`pow2` `cos-diff` `sub-neg` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

29.0ms	(* (sqrt (* K (+ m n))) (sqrt (* K (+ m n))))
3.0ms	(sqrt (* K (+ m n)))
3.0ms	(sqrt (* K (+ m n)))
49.0ms	(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

series183.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (sqrt (* K (+ m n))) (sqrt (* K (+ m n))))
48.0ms	(sqrt (* K (+ m n)))
52.0ms	(sqrt (* K (+ m n)))
53.0ms	(cos (- (/ (* (sqrt (* K (+ m n))) (sqrt (* K (+ m n)))) 2.0) M))

simplify42.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	254	656
1	959	575
2	5001	548

prune372.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.1b	(* (sqrt K) (* (sqrt K) (+ m n)))
0.1b	(* (sqrt K) (+ m n))
16.8b	(cos (- (/ (* (sqrt K) (* (sqrt K) (+ m n))) 2.0) M))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

31.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
16.0ms	(* (sqrt K) (* (sqrt K) (+ m n)))
11.0ms	(* (sqrt K) (+ m n))
36.0ms	(cos (- (/ (* (sqrt K) (* (sqrt K) (+ m n))) 2.0) M))

series532.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
39.0ms	(* (sqrt K) (* (sqrt K) (+ m n)))
76.0ms	(* (sqrt K) (+ m n))
147.0ms	(cos (- (/ (* (sqrt K) (* (sqrt K) (+ m n))) 2.0) M))

simplify53.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	473	625
1	1781	550
2	5002	547

prune395.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes136.0ms

Accuracy

0% (0.1b remaining)

Error of 1.2b against oracle of 1.1b and baseline of 1.2b

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

sample1.0s

Algorithm

intervals

Results

674.0ms	8139×	body	80	valid
23.0ms	44×	body	1280	valid
22.0ms	62×	body	640	valid
21.0ms	273×	body	80	overflowed
10.0ms	39×	body	320	valid
4.0ms	21×	body	160	valid