Details

sample382.0ms

Algorithm

intervals

Results

232.0ms	46×	body	640	valid
57.0ms	52×	body	1280	valid
25.0ms	145×	body	80	valid
13.0ms	25×	body	320	valid
6.0ms	52×	body	80	nan
6.0ms	18×	body	160	valid

simplify306.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

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

prune14.0ms

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: 16.4b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
7.6b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
22.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite57.0ms

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))
7.0ms	(* x (/ 1.0 (tan B)))
27.0ms	(* (/ 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)))

series135.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ F (sin B))
25.0ms	(* x (/ 1.0 (tan B)))
65.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
33.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify86.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (71.0ms)

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

prune379.0ms

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: 1.3b

Counts

167 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
0.3b	(* x (/ 1.0 (tan B)))
22.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite45.0ms

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:

11.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
12.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
7.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series139.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
34.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
24.0ms	(* x (/ 1.0 (tan B)))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	773	1380
1	3290	1264
2	5002	1264

prune312.0ms

Filtered

145 candidates to 107 candidates (26.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	146	12	158

Merged error: 1.3b

Counts

158 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
22.1b	(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:

5.0ms	(/ (* x 1.0) (tan B))
11.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
10.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series140.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (* x 1.0) (tan B))
59.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
31.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
26.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	726	1325
1	3045	1209
2	5001	1209

prune287.0ms

Filtered

134 candidates to 102 candidates (23.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	135	11	146

Merged error: 1.3b

Counts

146 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
22.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

192×	`times-frac`
112×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
51×	`unpow-prod-down`
29×	`associate-/l*`
25×	`add-exp-log`
17×	`sqr-pow`
16×	`add-cbrt-cube`
13×	`pow-unpow` `associate-/r*`
12×	`div-exp`
8×	`div-inv`
6×	`cbrt-undiv`
5×	`pow1`
4×	`add-log-exp`
3×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`tan-quot` `pow-pow` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`

Counts

4 → 214

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
9.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
16.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
8.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series214.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (* x 1.0) (tan B))
71.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
97.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
22.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify113.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1053	3341
1	4419	3207
2	5001	3207

prune524.0ms

Filtered

226 candidates to 181 candidates (19.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	224	13	237

Merged error: 1.3b

Counts

237 → 13

regimes363.0ms

Accuracy

98.7% (0.1b remaining)

Error of 1.5b against oracle of 1.3b and baseline of 12.5b

bsearch195.0ms

Steps

Iters	Range		Point
9	7.445930829423163e+152	1.3743068256281614e+158	1.33545010559267e+154
10	-7.462986351318234e+164	-2.743265733708822e+153	-1.3355631469912174e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	62
1	69	62

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	1657×	body	1280	valid
894.0ms	1442×	body	640	valid
647.0ms	4752×	body	80	valid
294.0ms	672×	body	320	valid
174.0ms	1715×	body	80	nan
101.0ms	350×	body	160	valid

Details

sample382.0ms

simplify306.0ms

prune14.0ms

localize27.0ms

rewrite57.0ms

series135.0ms

simplify86.0ms

prune379.0ms

localize24.0ms

rewrite45.0ms

series139.0ms

simplify85.0ms

prune312.0ms

localize23.0ms

rewrite40.0ms

series140.0ms

simplify77.0ms

prune287.0ms

localize22.0ms

rewrite48.0ms

series214.0ms

simplify113.0ms

prune524.0ms

regimes363.0ms

bsearch195.0ms

simplify3.0ms

end0.0ms

sample4.1s

Profiling