Details

sample42.0ms

Algorithm

intervals

Results

20.0ms	259×	body	80	valid
3.0ms	5×	body	1280	valid
1.0ms	4×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify48.0ms

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.7b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

24.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms	(* K (+ m n))
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series852.0ms

Counts

4 → 12

Calls

4 calls:

516.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
257.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
24.0ms	(* K (+ m n))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify48.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	489	871
1	1795	780
2	5001	777

prune354.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.6b

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)

rewrite33.0ms

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:

21.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series437.0ms

Counts

2 → 6

Calls

2 calls:

179.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
258.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify84.0ms

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

prune175.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.6b

localize25.0ms

Local error

Found 4 expressions with local error:

12.0b	(cbrt (* K (+ m n)))
12.0b	(cbrt (* K (+ m n)))
12.0b	(cbrt (* K (+ m n)))
33.6b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite24.0ms

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:

4.0ms	(cbrt (* K (+ m n)))
4.0ms	(cbrt (* K (+ m n)))
4.0ms	(cbrt (* K (+ m n)))
10.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series360.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (* K (+ m n)))
101.0ms	(cbrt (* K (+ m n)))
100.0ms	(cbrt (* K (+ m n)))
55.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify56.0ms

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

prune294.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.5b

localize30.0ms

Local error

Found 4 expressions with local error:

12.0b	(cbrt (* K (+ m n)))
12.0b	(cbrt (* K (+ m n)))
12.0b	(cbrt (* K (+ m n)))
33.7b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n)))))) 2.0) M))

rewrite37.0ms

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:

5.0ms	(cbrt (* K (+ m n)))
7.0ms	(cbrt (* K (+ m n)))
4.0ms	(cbrt (* K (+ m n)))
20.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n)))))) 2.0) M))

series363.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (* K (+ m n)))
110.0ms	(cbrt (* K (+ m n)))
99.0ms	(cbrt (* K (+ m n)))
52.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (* (cbrt (cbrt (* K (+ m n)))) (cbrt (cbrt (* K (+ m n))))) (cbrt (cbrt (* K (+ m n)))))) 2.0) M))

simplify60.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (54.0ms)

Iter	Nodes	Cost
0	194	672
1	390	600
2	844	576
3	2082	573
4	5002	564

prune336.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.5b

regimes284.0ms

Accuracy

0% (0.3b remaining)

Error of 1.6b against oracle of 1.3b and baseline of 1.6b

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

sample1.1s

Algorithm

intervals

Results

648.0ms	8063×	body	80	valid
63.0ms	124×	body	1280	valid
56.0ms	164×	body	640	valid
31.0ms	117×	body	320	valid
9.0ms	55×	body	160	valid
4.0ms	5×	body	2560	valid