Details

sample432.0ms

Algorithm

intervals

Results

50.0ms	50×	body	640	valid
40.0ms	43×	body	1280	valid
25.0ms	168×	body	80	valid
5.0ms	12×	body	320	valid
4.0ms	39×	body	80	nan
3.0ms	11×	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

prune17.0ms

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: 15.9b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
9.3b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
16.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite49.0ms

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×	`tan-quot` `frac-times` `associate-/r/` `*-commutative`
1×	`neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `un-div-inv`

Counts

4 → 155

Calls

4 calls:

3.0ms	(/ 1.0 (tan B))
7.0ms	(* x (/ 1.0 (tan B)))
20.0ms	(* (/ 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)))

series128.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (tan B))
23.0ms	(* x (/ 1.0 (tan B)))
62.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
32.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	817	1480
1	3336	1390
2	5001	1389

prune1.5s

Filtered

167 candidates to 128 candidates (23.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	154	13	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	13	168

Merged error: 1.1b

Counts

168 → 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))
0.2b	(* x (/ 1.0 (tan B)))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
16.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite40.0ms

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:

10.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
7.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series133.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
22.0ms	(* x (/ 1.0 (tan B)))
32.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
22.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (17.0ms)

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

prune1.3s

Filtered

145 candidates to 106 candidates (26.9%)

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: 1.1b

Counts

158 → 12

localize24.0ms

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))))
16.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite37.0ms

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

series128.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (* x 1.0) (tan B))
53.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
32.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
21.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify75.0ms

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	131	3	134
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	136	10	146

Merged error: 1.1b

Counts

146 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
16.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite43.0ms

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:

9.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
5.0ms	(/ (* x 1.0) (tan B))
13.0ms	(/ (/ 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))

series202.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
22.0ms	(/ (* x 1.0) (tan B))
90.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify109.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 1 (22.0ms)

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

prune2.9s

Filtered

226 candidates to 181 candidates (19.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	221	5	226
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	226	10	236

Merged error: 1.1b

Counts

236 → 10

regimes309.0ms

Accuracy

98.1% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 10.7b

bsearch274.0ms

Steps

Iters	Range		Point
5	1.9941900793343876e+154	6.527560984919275e+154	2.0304285442231992e+154
10	-9.890537988017573e+164	-1.5954363105956547e+149	-1.3380089926747265e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	64
1	78	64

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.5s	1694×	body	1280	valid
835.0ms	1446×	body	640	valid
600.0ms	4631×	body	80	valid
285.0ms	715×	body	320	valid
151.0ms	1664×	body	80	nan
90.0ms	340×	body	160	valid

Details

sample432.0ms

simplify43.0ms

prune17.0ms

localize25.0ms

rewrite49.0ms

series128.0ms

simplify84.0ms

prune1.5s

localize24.0ms

rewrite40.0ms

series133.0ms

simplify83.0ms

prune1.3s

localize24.0ms

rewrite37.0ms

series128.0ms

simplify75.0ms

prune1.2s

localize20.0ms

rewrite43.0ms

series202.0ms

simplify109.0ms

prune2.9s

regimes309.0ms

bsearch274.0ms

simplify2.0ms

end0.0ms

sample3.9s

Profiling