Details

sample438.0ms

Algorithm

intervals

Results

67.0ms	53×	body	1280	valid
28.0ms	43×	body	640	valid
20.0ms	147×	body	80	valid
9.0ms	22×	body	320	valid
6.0ms	57×	body	80	nan
2.0ms	8×	body	160	valid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	42	15
1	83	14
2	151	14
3	356	14
4	1063	14
5	5002	14

prune16.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 16.1b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
10.0b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 154

Calls

4 calls:

3.0ms	(/ F (sin B))
14.0ms	(* x (/ 1.0 (tan B)))
13.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
12.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series139.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ F (sin B))
27.0ms	(* x (/ 1.0 (tan B)))
67.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
34.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	813	1470
1	3354	1381
2	5001	1380

prune1.5s

Filtered

166 candidates to 126 candidates (24.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	153	13	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	13	167

Merged error: 1.2b

Counts

167 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (/ 1.0 (tan B)))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
0.6b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

7.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
10.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
11.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series144.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* x (/ 1.0 (tan B)))
33.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
63.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify86.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	773	1380
1	3290	1264
2	5001	1264

prune1.3s

Filtered

145 candidates to 106 candidates (26.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	147	11	158

Merged error: 1.2b

Counts

158 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
0.6b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

4.0ms	(/ (* x 1.0) (tan B))
10.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
12.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series144.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (* x 1.0) (tan B))
32.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
63.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	726	1327
1	3050	1209
2	5001	1209

prune1.2s

Filtered

134 candidates to 102 candidates (23.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	135	10	145

Merged error: 1.2b

Counts

145 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
17.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-cbrt-cube`
15×	`times-frac`
13×	`pow-unpow`
7×	`unpow-prod-down` `associate-r` `prod-exp`
6×	`div-exp`
5×	`pow1`
4×	`cbrt-undiv` `associate-/r` `associate-/l` `add-log-exp`
3×	`pow-to-exp` `associate-l` `pow-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num`
1×	`tan-quot` `pow-pow` `associate-/r/` `*-commutative`

Counts

4 → 97

Calls

4 calls:

4.0ms	(/ (* x 1.0) (tan B))
9.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
10.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series214.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (* x 1.0) (tan B))
103.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
64.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	657	1115
1	2821	993
2	5001	993

prune778.0ms

Filtered

109 candidates to 83 candidates (23.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	108	11	119

Merged error: 1.2b

Counts

119 → 11

regimes336.0ms

Accuracy

88.6% (1.1b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 10.6b

bsearch315.0ms

Steps

Iters	Range		Point
7	1.0227793415615586e+152	1.8983365774941352e+154	1.3264063080845111e+154
10	-5.295777315019656e+206	-6.60621925885507e+187	-6.712874546376408e+187

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	63
1	73	63

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.4s	1645×	body	1280	valid
807.0ms	1404×	body	640	valid
615.0ms	4745×	body	80	valid
296.0ms	733×	body	320	valid
147.0ms	1588×	body	80	nan
91.0ms	338×	body	160	valid

Details

sample438.0ms

simplify43.0ms

prune16.0ms

localize25.0ms

rewrite50.0ms

series139.0ms

simplify84.0ms

prune1.5s

localize23.0ms

rewrite43.0ms

series144.0ms

simplify86.0ms

prune1.3s

localize22.0ms

rewrite40.0ms

series144.0ms

simplify74.0ms

prune1.2s

localize23.0ms

rewrite35.0ms

series214.0ms

simplify67.0ms

prune778.0ms

regimes336.0ms

bsearch315.0ms

simplify2.0ms

end0.0ms

sample3.9s

Profiling