Details

sample49.0ms

Algorithm

intervals

Results

24.0ms	257×	body	80	valid
2.0ms	4×	body	1280	valid
1.0ms	3×	body	640	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	320	valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (10.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize27.0ms

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)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

212.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
9.0ms	(- (/ (* K (+ m n)) 2.0) M)
33.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
15.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series548.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
58.0ms	(- (/ (* K (+ m n)) 2.0) M)
259.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
53.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify135.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	368	603
1	1045	563
2	4794	552
3	5001	552

prune304.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.0b

localize15.0ms

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)

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

212.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
36.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series446.0ms

Counts

2 → 6

Calls

2 calls:

178.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
267.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify85.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	253	368
1	720	351
2	2937	346
3	5002	343

prune159.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos (/ (* K (+ m n)) 2.0)) (cos M)) (* (sin (/ (* K (+ m n)) 2.0)) (sin (- M))))
0.2b	(* (sin (/ (* K (+ m n)) 2.0)) (sin (- M)))
39.6b	(sin (/ (* K (+ m n)) 2.0))
39.8b	(cos (/ (* K (+ m n)) 2.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`associate-r` `associate-l` `sin-mult`
2×	`cos-mult`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `sin-neg` `*-commutative` `distribute-rgt-neg-out` `frac-sub` `flip--` `cbrt-unprod` `sub-div` `unswap-sqr`

Counts

4 → 48

Calls

4 calls:

5.0ms	(- (* (cos (/ (* K (+ m n)) 2.0)) (cos M)) (* (sin (/ (* K (+ m n)) 2.0)) (sin (- M))))
8.0ms	(* (sin (/ (* K (+ m n)) 2.0)) (sin (- M)))
2.0ms	(sin (/ (* K (+ m n)) 2.0))
2.0ms	(cos (/ (* K (+ m n)) 2.0))

series241.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(- (* (cos (/ (* K (+ m n)) 2.0)) (cos M)) (* (sin (/ (* K (+ m n)) 2.0)) (sin (- M))))
60.0ms	(* (sin (/ (* K (+ m n)) 2.0)) (sin (- M)))
26.0ms	(sin (/ (* K (+ m n)) 2.0))
16.0ms	(cos (/ (* K (+ m n)) 2.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	226	677
1	691	604
2	2390	575
3	5001	568

prune343.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize56.0ms

Local error

Found 4 expressions with local error:

39.6b	(sin (/ (* K (+ m n)) 2.0))
39.8b	(cos (/ (* K (+ m n)) 2.0))
39.8b	(cos (/ (* K (+ m n)) 2.0))
39.8b	(cos (/ (* K (+ m n)) 2.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

1.0ms	(sin (/ (* K (+ m n)) 2.0))
1.0ms	(cos (/ (* K (+ m n)) 2.0))
1.0ms	(cos (/ (* K (+ m n)) 2.0))
2.0ms	(cos (/ (* K (+ m n)) 2.0))

series75.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(sin (/ (* K (+ m n)) 2.0))
20.0ms	(cos (/ (* K (+ m n)) 2.0))
15.0ms	(cos (/ (* K (+ m n)) 2.0))
16.0ms	(cos (/ (* K (+ m n)) 2.0))

simplify121.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	56	236
1	88	199
2	113	199
3	124	199
4	158	199
5	236	199
6	761	199
7	2328	199
8	5001	199

prune352.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.0b

regimes151.0ms

Accuracy

0% (0.1b remaining)

Error of 1.5b against oracle of 1.4b and baseline of 1.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

648.0ms	8052×	body	80	valid
68.0ms	140×	body	1280	valid
48.0ms	142×	body	640	valid
31.0ms	110×	body	320	valid
14.0ms	64×	body	160	valid
1.0ms	1×	body	2560	valid