Details

sample389.0ms

Algorithm

intervals

Results

55.0ms	58×	body	1280	valid
29.0ms	47×	body	640	valid
21.0ms	149×	body	80	valid
11.0ms	25×	body	320	valid
7.0ms	47×	body	80	nan
4.0ms	11×	body	160	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (18.0ms)

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

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 12.2b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.0b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite43.0ms

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:

4.0ms	(/ 1.0 (tan B))
7.0ms	(* x (/ 1.0 (tan B)))
14.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
13.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series589.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1.0 (tan B))
111.0ms	(* x (/ 1.0 (tan B)))
284.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
159.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	767	1428
1	3183	1338
2	5001	1337

prune583.0ms

Filtered

167 candidates to 129 candidates (77.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	157	10	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	158	10	168

Merged error: 0.0b

Counts

168 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.3b	(* x (/ 1.0 (tan B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 174

Calls

4 calls:

14.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
7.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series925.0ms

Counts

4 → 12

Calls

4 calls:

352.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
107.0ms	(* x (/ 1.0 (tan B)))
320.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
146.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify97.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	848	2078
1	3742	1960
2	5001	1960

prune583.0ms

Filtered

186 candidates to 143 candidates (76.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	187	9	196

Merged error: 0.0b

Counts

196 → 9

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) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
14.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
13.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series910.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (* x 1.0) (tan B))
346.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
310.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
145.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify94.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	801	2023
1	3498	1905
2	5001	1905

prune557.0ms

Filtered

175 candidates to 137 candidates (78.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	172	3	175
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	176	8	184

Merged error: 0.0b

Counts

184 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
77×	`add-sqr-sqrt`
67×	`add-cube-cbrt` `*-un-lft-identity`
41×	`add-exp-log`
30×	`pow-unpow`
25×	`unpow-prod-down` `associate-r`
20×	`add-cbrt-cube`
18×	`div-exp`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-/r` `associate-/l`
9×	`div-inv` `sqr-pow`
8×	`pow1`
7×	`cbrt-undiv` `prod-exp`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `rec-exp` `1-exp` `associate-l` `pow-exp` `cbrt-unprod`
2×	`neg-sub0` `pow-neg` `frac-2neg` `clear-num` `associate-/l/` `pow-sub`
1×	`neg-mul-1` `pow-flip` `pow-pow` `associate-r/` `pow-prod-down` `associate-/r/` `-commutative` `inv-pow`

Counts

4 → 197

Calls

4 calls:

14.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
6.0ms	(/ 1 (/ (tan B) (* x 1.0)))
10.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series905.0ms

Counts

4 → 12

Calls

4 calls:

354.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
87.0ms	(/ 1 (/ (tan B) (* x 1.0)))
317.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
147.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify112.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	944	2306
1	4409	2151
2	5002	2112

prune579.0ms

Filtered

209 candidates to 145 candidates (69.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	209	8	217

Merged error: 0.0b

Counts

217 → 8

regimes135.0ms

Accuracy

97.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.3b

bsearch266.0ms

Steps

Iters	Range		Point
8	1538.2388859235716	3249381.761613268	243770.40142476148
8	-215280256.6145876	-5131.2843345437395	-12552003.890338559

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	40
1	56	40

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	1686×	body	1280	valid
865.0ms	1406×	body	640	valid
659.0ms	4682×	body	80	valid
317.0ms	722×	body	320	valid
158.0ms	1597×	body	80	nan
103.0ms	357×	body	160	valid

Details

sample389.0ms

simplify61.0ms

prune11.0ms

localize26.0ms

rewrite43.0ms

series589.0ms

simplify85.0ms

prune583.0ms

localize27.0ms

rewrite48.0ms

series925.0ms

simplify97.0ms

prune583.0ms

localize23.0ms

rewrite48.0ms

series910.0ms

simplify94.0ms

prune557.0ms

localize28.0ms

rewrite48.0ms

series905.0ms

simplify112.0ms

prune579.0ms

regimes135.0ms

bsearch266.0ms

simplify2.0ms

end0.0ms

sample4.0s

Profiling