Details

sample45.0ms

Algorithm

intervals

Results

21.0ms	260×	body	80	valid
6.0ms	5×	body	1280	valid
1.0ms	3×	body	640	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	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: 13.5b

Counts

2 → 1

localize22.0ms

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))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
36.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

198×	`add-sqr-sqrt`
167×	`*-un-lft-identity`
150×	`prod-diff`
81×	`add-cube-cbrt`
78×	`unpow-prod-down`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
51×	`difference-of-squares`
43×	`distribute-lft-out--`
24×	`fma-neg`
23×	`cos-sum`
22×	`times-frac`
14×	`add-log-exp`
13×	`sqr-pow`
11×	`associate--r+`
7×	`pow1` `add-exp-log`
6×	`neg-mul-1` `diff-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`sub-neg` `pow-unpow` `associate-l` `div-inv`
2×	`associate-*r/` `neg-log`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr`

Counts

4 → 259

Calls

4 calls:

31.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
6.0ms	(* K (+ m n))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
12.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series544.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
24.0ms	(* K (+ m n))
256.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify167.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	991	6064
1	2883	4404
2	5001	4329

prune755.0ms

Filtered

271 candidates to 116 candidates (42.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	268	3	271
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	269	3	272

Merged error: 0.6b

Counts

272 → 3

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)

rewrite57.0ms

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:

32.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series627.0ms

Counts

2 → 6

Calls

2 calls:

363.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
264.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify78.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (45.0ms)

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

prune375.0ms

Filtered

207 candidates to 71 candidates (34.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	207	3	210

Merged error: 0.6b

Counts

210 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
0.5b	(* (cbrt (+ m n)) (cbrt (+ m n)))
36.1b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
35×	`add-sqr-sqrt`
32×	`cbrt-prod`
27×	`add-cube-cbrt`
23×	`cos-sum`
21×	`prod-diff`
16×	`cbrt-div`
11×	`pow1`
9×	`times-frac` `swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `cos-diff` `sub-neg` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 120

Calls

4 calls:

3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
11.0ms	(* (cbrt (+ m n)) (cbrt (+ m n)))
22.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series512.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt (+ m n))
129.0ms	(cbrt (+ m n))
158.0ms	(* (cbrt (+ m n)) (cbrt (+ m n)))
100.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify67.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	552	2076
1	1550	1778
2	5001	1730

prune584.0ms

Filtered

132 candidates to 83 candidates (62.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	131	4	135

Merged error: 0.6b

Counts

135 → 4

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cbrt (+ m n)))
0.5b	(cbrt (cbrt (+ m n)))
0.6b	(* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n))))
35.9b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))) (cbrt (cbrt (+ m n))))) 2.0) M))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

92×	`cbrt-prod`
51×	`add-sqr-sqrt` `*-un-lft-identity`
33×	`add-cube-cbrt`
32×	`cbrt-div`
23×	`cos-sum`
21×	`prod-diff`
12×	`swap-sqr`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`times-frac` `unswap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `cos-diff` `sub-neg` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 140

Calls

4 calls:

4.0ms	(cbrt (cbrt (+ m n)))
4.0ms	(cbrt (cbrt (+ m n)))
14.0ms	(* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n))))
38.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))) (cbrt (cbrt (+ m n))))) 2.0) M))

series777.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(cbrt (cbrt (+ m n)))
196.0ms	(cbrt (cbrt (+ m n)))
277.0ms	(* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n))))
101.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))) (cbrt (cbrt (+ m n))))) 2.0) M))

simplify72.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	591	3198
1	1598	2816
2	5001	2723

prune752.0ms

Filtered

152 candidates to 96 candidates (63.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	149	3	152
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	152	4	156

Merged error: 0.6b

Counts

156 → 4

regimes188.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

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

692.0ms	8087×	body	80	valid
67.0ms	132×	body	1280	valid
57.0ms	145×	body	640	valid
29.0ms	108×	body	320	valid
7.0ms	43×	body	160	valid
2.0ms	2×	body	2560	valid