Details

analyze1.9s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

sample137.0ms

Algorithm

intervals

Results

54.0ms	58×	body	1280	valid
29.0ms	46×	body	640	valid
17.0ms	113×	body	80	valid
13.0ms	29×	body	320	valid
4.0ms	27×	body	80	invalid
3.0ms	10×	body	160	valid
1.0ms	6×	body	80	nan

simplify454.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4951	26
1	4951	26

prune16.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 9.9b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
0.4b	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
17.5b	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

70×	`times-frac`
62×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
34×	`pow-unpow`
17×	`add-exp-log`
15×	`unpow-prod-down`
14×	`associate-r`
13×	`add-cbrt-cube`
10×	`associate-/l*`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
7×	`pow1`
6×	`associate-/r*`
5×	`div-exp` `sqr-pow`
4×	`div-inv` `add-log-exp`
3×	`cbrt-undiv` `neg-mul-1` `associate-l`
2×	`tan-quot` `neg-sub0` `pow-to-exp` `pow-neg` `frac-2neg` `div-sub` `distribute-frac-neg` `pow-exp` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `associate-/l/` `pow-sub` `unswap-sqr`
1×	`pow-pow` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 158

Calls

4 calls:

3.0ms	(/ 1.0 (tan B))
7.0ms	(* x (/ 1.0 (tan B)))
22.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
12.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

series155.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (tan B))
24.0ms	(* x (/ 1.0 (tan B)))
90.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
31.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4939	2748
1	4939	2748

prune445.0ms

Filtered

135 candidates to 170 candidates (-25.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	151	19	170
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	152	20	172

Merged error: 9.6b

Counts

172 → 20

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
0.4b	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
17.5b	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
68×	`add-sqr-sqrt`
58×	`add-cube-cbrt` `*-un-lft-identity`
34×	`pow-unpow`
25×	`add-exp-log` `unpow-prod-down` `associate-r`
16×	`add-cbrt-cube`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqr-pow`
8×	`div-exp` `associate-/l*`
7×	`pow1`
6×	`associate-/r*`
5×	`prod-exp`
4×	`cbrt-undiv` `div-inv` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `neg-mul-1` `associate-l` `pow-exp` `cbrt-unprod`
2×	`neg-sub0` `pow-neg` `frac-2neg` `div-sub` `distribute-frac-neg` `clear-num` `associate-/l/` `pow-sub`
1×	`tan-quot` `pow-pow` `associate-r/` `pow-prod-down` `associate-/r/` `-commutative`

Counts

4 → 167

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
14.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
9.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
9.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

series220.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (* x 1.0) (tan B))
90.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
83.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
24.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4952	3595
1	4952	3595

prune459.0ms

Filtered

140 candidates to 179 candidates (-27.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	176	3	179
Fresh	1	18	19
Picked	1	0	1
Done	0	0	0
Total	178	21	199

Merged error: 9.6b

Counts

199 → 21

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
0.3b	(* (/ x (sin B)) (cos B))
0.4b	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
17.5b	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

85×	`times-frac`
79×	`add-sqr-sqrt`
64×	`add-cube-cbrt` `*-un-lft-identity`
34×	`pow-unpow`
28×	`associate-r`
25×	`add-exp-log` `unpow-prod-down`
16×	`associate-l` `add-cbrt-cube`
9×	`pow1` `distribute-lft-neg-in` `distribute-rgt-neg-in` `sqr-pow`
7×	`div-exp` `associate-/l*`
6×	`prod-exp` `unswap-sqr`
4×	`cbrt-unprod` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `neg-mul-1` `pow-exp` `associate-/r*`
2×	`neg-sub0` `pow-neg` `div-sub` `distribute-frac-neg` `pow-prod-down` `*-commutative` `associate-/l/` `pow-sub`
1×	`pow-pow` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 177

Calls

4 calls:

15.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
6.0ms	(* (/ x (sin B)) (cos B))
9.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
10.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

series214.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
17.0ms	(* (/ x (sin B)) (cos B))
85.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
21.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4949	3698
1	4949	3698

prune477.0ms

Filtered

149 candidates to 189 candidates (-26.8%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	185	4	189
Fresh	4	16	20
Picked	0	1	1
Done	0	0	0
Total	189	21	210

Merged error: 9.6b

Counts

210 → 21

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sin B)) (cos B))
0.2b	(* x (* (/ 1.0 (sin B)) (cos B)))
0.4b	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
17.5b	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

61×	`times-frac`
55×	`add-sqr-sqrt`
50×	`add-cube-cbrt` `*-un-lft-identity`
34×	`pow-unpow`
24×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`associate-l`
15×	`unpow-prod-down`
12×	`pow1`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
7×	`prod-exp` `cbrt-unprod` `associate-/l*`
5×	`div-exp` `sqr-pow`
4×	`associate-r` `pow-prod-down` `add-log-exp`
3×	`cbrt-undiv` `neg-mul-1` `associate-/r*` `div-inv`
2×	`neg-sub0` `pow-to-exp` `pow-neg` `div-sub` `distribute-frac-neg` `associate-l/` `pow-exp` `-commutative` `associate-/l/` `pow-sub` `unswap-sqr`
1×	`pow-pow` `frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 150

Calls

4 calls:

6.0ms	(* (/ 1.0 (sin B)) (cos B))
6.0ms	(* x (* (/ 1.0 (sin B)) (cos B)))
11.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
9.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

series132.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (/ 1.0 (sin B)) (cos B))
18.0ms	(* x (* (/ 1.0 (sin B)) (cos B)))
85.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
21.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4954	2798
1	4954	2798

prune311.0ms

Filtered

126 candidates to 162 candidates (-28.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	11	8	19
Picked	0	1	1
Done	0	1	1
Total	171	12	183

Merged error: 1.0b

Counts

183 → 12

regimes440.0ms

Accuracy

97.4% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 10.7b

bsearch166.0ms

Steps

Iters	Range		Point
8	1.2993448350525277e+154	3.9645714826741013e+158	1.3747026542039707e+154
10	-3.0820891573076253e+166	-1.0058130669613105e+151	-1.3733114268899944e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	208	125
1	208	125

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.6s	1722×	body	1280	valid
836.0ms	1397×	body	640	valid
532.0ms	3845×	body	80	valid
287.0ms	675×	body	320	valid
108.0ms	361×	body	160	valid
91.0ms	645×	body	80	invalid
13.0ms	134×	body	80	nan
1.0ms	1×	body	640	invalid

Details

analyze1.9s

sample137.0ms

simplify454.0ms

prune16.0ms

localize26.0ms

rewrite51.0ms

series155.0ms

simplify67.0ms

prune445.0ms

localize23.0ms

rewrite43.0ms

series220.0ms

simplify69.0ms

prune459.0ms

localize25.0ms

rewrite47.0ms

series214.0ms

simplify71.0ms

prune477.0ms

localize24.0ms

rewrite38.0ms

series132.0ms

simplify64.0ms

prune311.0ms

regimes440.0ms

bsearch166.0ms

simplify3.0ms

end0.0ms

sample3.7s

Profiling