Details

sample66.0ms

Algorithm

intervals

Results

38.0ms	252×	body	80	valid
5.0ms	8×	body	640	valid
2.0ms	5×	body	320	valid
2.0ms	2×	body	1280	valid
1.0ms	1×	body	2560	valid
0.0ms	1×	body	160	valid

simplify51.0ms

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: 16.9b

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)
0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
38.0b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite622.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`unpow-prod-down` `diff-log` `add-cbrt-cube`
4×	`associate-r`
3×	`sub-neg` `pow-unpow` `associate-l` `difference-of-squares`
2×	`cos-sum` `distribute-rgt-neg-in` `associate-*r/` `neg-log` `associate--r+`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

9.0ms	(* K (+ m n))
33.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
562.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
15.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series549.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* K (+ m n))
293.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
175.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	435	667
1	1447	621
2	5002	620

prune370.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.6b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite593.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`add-log-exp`
11×	`add-sqr-sqrt`
7×	`distribute-lft-out--`
6×	`unpow-prod-down` `diff-log`
4×	`add-cube-cbrt`
3×	`pow1` `add-exp-log` `pow-unpow` `difference-of-squares`
2×	`sub-neg` `distribute-rgt-neg-in` `neg-log` `add-cbrt-cube` `associate--r+`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `times-frac` `pow-exp` `flip--` `associate--r-` `sqr-pow`

Counts

2 → 44

Calls

2 calls:

33.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
558.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series446.0ms

Counts

2 → 6

Calls

2 calls:

263.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
183.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify82.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	277	469
1	798	444
2	3368	435
3	5001	432

prune181.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.6b

localize26.0ms

Local error

Found 4 expressions with local error:

17.0b	(cbrt (* K (+ m n)))
17.0b	(cbrt (* K (+ m n)))
17.0b	(cbrt (* K (+ m n)))
38.2b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*r/`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 43

Calls

4 calls:

3.0ms	(cbrt (* K (+ m n)))
3.0ms	(cbrt (* K (+ m n)))
3.0ms	(cbrt (* K (+ m n)))
30.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series368.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (* K (+ m n)))
108.0ms	(cbrt (* K (+ m n)))
101.0ms	(cbrt (* K (+ m n)))
53.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify54.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (48.0ms)

Iter	Nodes	Cost
0	186	496
1	357	446
2	740	422
3	1608	419
4	5001	407

prune313.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.5b

localize32.0ms

Local error

Found 4 expressions with local error:

17.0b	(cbrt (* K (+ m n)))
17.0b	(cbrt (* K (+ m n)))
17.0b	(cbrt (* K (+ m n)))
38.2b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n)))))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite343.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*r/`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 43

Calls

4 calls:

3.0ms	(cbrt (* K (+ m n)))
3.0ms	(cbrt (* K (+ m n)))
3.0ms	(cbrt (* K (+ m n)))
332.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n)))))) (cbrt (* K (+ m n)))) 2.0) M))

series372.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (* K (+ m n)))
103.0ms	(cbrt (* K (+ m n)))
106.0ms	(cbrt (* K (+ m n)))
59.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n)))))) (cbrt (* K (+ m n)))) 2.0) M))

simplify60.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (53.0ms)

Iter	Nodes	Cost
0	195	672
1	384	600
2	836	576
3	2119	573
4	5002	564

prune353.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.5b

regimes289.0ms

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	21	10
1	23	10
2	23	10

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.1s	8117×	body	80	valid
84.0ms	152×	body	640	valid
75.0ms	98×	body	1280	valid
44.0ms	99×	body	320	valid
13.0ms	47×	body	160	valid
4.0ms	4×	body	2560	valid