Details

sample42.0ms

Algorithm

intervals

Results

21.0ms	255×	body	80	valid
3.0ms	5×	body	1280	valid
1.0ms	2×	body	640	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	320	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	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

localize27.0ms

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))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
23×	`add-cube-cbrt` `cos-sum`
21×	`prod-diff`
13×	`times-frac`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`pow1`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `associate-r/` `associate-r*` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-unpow` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `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` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `unswap-sqr` `sqr-pow`

Counts

4 → 105

Calls

4 calls:

10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms	(* K (+ m n))
7.0ms	(/ (* K (+ m n)) 2.0)
11.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series393.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
28.0ms	(* K (+ m n))
41.0ms	(/ (* K (+ m n)) 2.0)
58.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify65.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	634	1318
1	2180	1071
2	5001	1070

prune373.0ms

Filtered

117 candidates to 75 candidates (64.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	4	118

Merged error: 0.6b

Counts

118 → 4

localize14.0ms

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)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
148×	`*-un-lft-identity`
129×	`prod-diff`
78×	`unpow-prod-down`
64×	`add-cube-cbrt`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
51×	`difference-of-squares`
43×	`distribute-lft-out--`
24×	`fma-neg`
13×	`times-frac` `sqr-pow`
12×	`add-log-exp`
11×	`associate--r+`
6×	`neg-mul-1` `diff-log`
3×	`pow1` `add-exp-log` `pow-unpow`
2×	`expm1-log1p-u` `sub-neg` `neg-log` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `flip--` `associate--r-`

Counts

2 → 201

Calls

2 calls:

29.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series448.0ms

Counts

2 → 6

Calls

2 calls:

188.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
260.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify87.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	608	5050
1	1693	3609
2	5001	3001

prune306.0ms

Filtered

207 candidates to 71 candidates (34.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	207	4	211

Merged error: 0.6b

Counts

211 → 4

localize29.0ms

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))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
95×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
65×	`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`
5×	`cos-sum`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`prod-diff`
2×	`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 → 187

Calls

4 calls:

22.0ms	(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
7.0ms	(/ (+ m n) (sqrt 2.0))
4.0ms	(/ K (sqrt 2.0))
13.0ms	(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

series670.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
92.0ms	(/ (+ m n) (sqrt 2.0))
60.0ms	(/ K (sqrt 2.0))
332.0ms	(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

simplify72.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	599	1597
1	2634	1463
2	5001	1399

prune682.0ms

Filtered

199 candidates to 123 candidates (61.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	199	4	203

Merged error: 0.6b

Counts

203 → 4

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
32.0b	(cos (- (* (* (/ (cbrt K) (/ (fabs (cbrt 2.0)) (cbrt K))) (/ (cbrt K) (sqrt (cbrt 2.0)))) (/ (+ m n) (sqrt 2.0))) M))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`cos-sum`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `prod-diff`
1×	`cos-diff` `sub-neg`

Counts

4 → 54

Calls

4 calls:

1.0ms	(cbrt K)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
29.0ms	(cos (- (* (* (/ (cbrt K) (/ (fabs (cbrt 2.0)) (cbrt K))) (/ (cbrt K) (sqrt (cbrt 2.0)))) (/ (+ m n) (sqrt 2.0))) M))

series1.1s

Counts

4 → 8

Calls

4 calls:

192.0ms	(cbrt K)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
905.0ms	(cos (- (* (* (/ (cbrt K) (/ (fabs (cbrt 2.0)) (cbrt K))) (/ (cbrt K) (sqrt (cbrt 2.0)))) (/ (+ m n) (sqrt 2.0))) M))

simplify64.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	239	705
1	582	634
2	1807	628
3	5001	625

prune349.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	62	4	66

Merged error: 0.6b

Counts

66 → 4

regimes188.0ms

Accuracy

0% (0.1b 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

sample1.1s

Algorithm

intervals

Results

704.0ms	8109×	body	80	valid
49.0ms	96×	body	1280	valid
45.0ms	127×	body	640	valid
27.0ms	101×	body	320	valid
9.0ms	46×	body	160	valid