Details

sample42.0ms

Algorithm

intervals

Results

21.0ms	255×	body	80	valid
2.0ms	5×	body	1280	valid
1.0ms	2×	body	640	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	320	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

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 12.5b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
0.2b	(/ (* K (+ m n)) 2.0)
31.9b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms	(* K (+ m n))
7.0ms	(/ (* K (+ m n)) 2.0)
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series376.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
25.0ms	(* K (+ m n))
40.0ms	(/ (* K (+ m n)) 2.0)
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify54.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	411	487
1	1722	437
2	5001	437

prune322.0ms

Filtered

88 candidates to 63 candidates (71.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 0.6b

Counts

89 → 4

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))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series433.0ms

Counts

2 → 6

Calls

2 calls:

180.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
253.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify83.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (77.0ms)

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

prune151.0ms

Filtered

50 candidates to 34 candidates (68.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	50	4	54

Merged error: 0.6b

Counts

54 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
0.4b	(/ (+ m n) (sqrt 2.0))
0.5b	(/ K (sqrt 2.0))
31.9b	(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
94×	`add-sqr-sqrt`
90×	`*-un-lft-identity`
64×	`add-cube-cbrt`
54×	`sqrt-prod`
28×	`associate-r`
22×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out`
12×	`associate-/r*`
9×	`unswap-sqr`
7×	`associate-/l*`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`cos-sum` `frac-2neg` `clear-num` `associate-/l/`
1×	`cos-diff` `frac-times` `sub-neg` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 176

Calls

4 calls:

21.0ms	(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
6.0ms	(/ (+ m n) (sqrt 2.0))
4.0ms	(/ K (sqrt 2.0))
12.0ms	(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

series625.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
86.0ms	(/ (+ m n) (sqrt 2.0))
55.0ms	(/ K (sqrt 2.0))
310.0ms	(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

simplify63.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	529	1443
1	2467	1336
2	5002	1280

prune622.0ms

Filtered

188 candidates to 114 candidates (60.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	185	3	188
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	188	4	192

Merged error: 0.6b

Counts

192 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(/ 1 (* (fabs (cbrt 2.0)) 1))
32.0b	(cos (- (* (* (/ 1 (* (fabs (cbrt 2.0)) 1)) (/ K (sqrt (cbrt 2.0)))) (/ (+ m n) (sqrt 2.0))) M))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`cbrt-prod` `1-exp` `div-exp` `prod-exp`
4×	`add-log-exp`
3×	`rec-exp` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `cos-sum` `pow-flip` `pow1/3`
1×	`cos-diff` `sub-neg` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `inv-pow`

Counts

4 → 63

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
5.0ms	(/ 1 (* (fabs (cbrt 2.0)) 1))
17.0ms	(cos (- (* (* (/ 1 (* (fabs (cbrt 2.0)) 1)) (/ K (sqrt (cbrt 2.0)))) (/ (+ m n) (sqrt 2.0))) M))

series962.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(/ 1 (* (fabs (cbrt 2.0)) 1))
961.0ms	(cos (- (* (* (/ 1 (* (fabs (cbrt 2.0)) 1)) (/ K (sqrt (cbrt 2.0)))) (/ (+ m n) (sqrt 2.0))) M))

simplify55.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	243	567
1	692	510
2	1955	498
3	5001	497

prune288.0ms

Filtered

69 candidates to 44 candidates (63.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	69	4	73

Merged error: 0.6b

Counts

73 → 4

regimes170.0ms

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

sample1.2s

Algorithm

intervals

Results

713.0ms	8109×	body	80	valid
50.0ms	96×	body	1280	valid
47.0ms	127×	body	640	valid
26.0ms	101×	body	320	valid
8.0ms	46×	body	160	valid