Details

sample438.0ms

Algorithm

intervals

Results

66.0ms	52×	body	1280	valid
30.0ms	50×	body	640	valid
21.0ms	153×	body	80	valid
12.0ms	29×	body	320	valid
6.0ms	57×	body	80	nan
5.0ms	9×	body	160	valid

simplify48.0ms

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

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: 14.3b

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)))
5.7b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
17.4b	(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×	`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)))
21.0ms	(* (/ 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)))

series610.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ F (sin B))
111.0ms	(* x (/ 1.0 (tan B)))
295.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
156.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify91.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	765	1416
1	3206	1325
2	5002	1324

prune582.0ms

Filtered

166 candidates to 126 candidates (75.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	151	15	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	152	15	167

Merged error: 0.0b

Counts

167 → 15

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))
17.4b	(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:

7.0ms	(* x (/ 1.0 (tan B)))
13.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
11.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series809.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* x (/ 1.0 (tan B)))
208.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
347.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
144.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	721	1298
1	3136	1178
2	5001	1178

prune454.0ms

Filtered

145 candidates to 108 candidates (74.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	138	7	145
Fresh	7	7	14
Picked	1	0	1
Done	0	0	0
Total	146	14	160

Merged error: 0.0b

Counts

160 → 14

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 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))
17.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite38.0ms

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))))
11.0ms	(/ (* 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)))

series806.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (* x 1.0) (tan B))
206.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
346.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
146.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify73.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	674	1243
1	2891	1123
2	5002	1123

prune420.0ms

Filtered

134 candidates to 101 candidates (75.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	136	12	148

Merged error: 0.0b

Counts

148 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
17.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite39.0ms

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:

5.0ms	(/ (* x 1.0) (tan B))
10.0ms	(/ 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))

series783.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (* x 1.0) (tan B))
297.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
248.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
131.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	608	1033
1	2584	921
2	5001	921

prune309.0ms

Filtered

109 candidates to 83 candidates (76.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	110	11	121

Merged error: 0.0b

Counts

121 → 11

regimes177.0ms

Accuracy

98.1% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.7b

bsearch323.0ms

Steps

Iters	Range		Point
10	4.41326808055529	1.1947926814984866e+17	23539.691591104813
10	-4.045893515159076e+21	-63661563329.20501	-66669777482.95108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	36
1	55	36

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	1698×	body	1280	valid
801.0ms	1390×	body	640	valid
631.0ms	4802×	body	80	valid
280.0ms	693×	body	320	valid
160.0ms	1633×	body	80	nan
96.0ms	357×	body	160	valid

Details

sample438.0ms

simplify48.0ms

prune11.0ms

localize25.0ms

rewrite49.0ms

series610.0ms

simplify91.0ms

prune582.0ms

localize23.0ms

rewrite45.0ms

series809.0ms

simplify84.0ms

prune454.0ms

localize26.0ms

rewrite38.0ms

series806.0ms

simplify73.0ms

prune420.0ms

localize21.0ms

rewrite39.0ms

series783.0ms

simplify71.0ms

prune309.0ms

regimes177.0ms

bsearch323.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling