Details

sample5.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.321533%

Guaranteed chance to sample good point: 34.215554%

Results

57.0ms	57×	body	1280	valid
32.0ms	50×	body	640	valid
17.0ms	117×	body	80	valid
10.0ms	23×	body	320	valid
3.0ms	20×	body	80	invalid
3.0ms	9×	body	160	valid
0.0ms	1×	body	80	nan

simplify382.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (17.0ms)

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: 10.4b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
4.8b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
14.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite41.0ms

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

series134.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (tan B))
27.0ms	(* x (/ 1.0 (tan B)))
58.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
38.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (67.0ms)

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

prune404.0ms

Filtered

128 candidates to 167 candidates (-30.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	152	15	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	15	168

Merged error: 0.8b

Counts

168 → 15

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* x (/ 1.0 (tan B)))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
14.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

9.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
7.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
8.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series202.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
22.0ms	(* x (/ 1.0 (tan B)))
61.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
22.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	703	1170
1	3086	1048
2	5001	1048

prune285.0ms

Filtered

91 candidates to 120 candidates (-31.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	112	8	120
Fresh	7	7	14
Picked	1	0	1
Done	0	0	0
Total	120	15	135

Merged error: 0.8b

Counts

135 → 15

localize23.0ms

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)))
14.7b	(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)))
8.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series202.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (* x 1.0) (tan B))
96.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
61.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
22.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (14.0ms)

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

prune247.0ms

Filtered

82 candidates to 109 candidates (-32.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	110	14	124

Merged error: 0.8b

Counts

124 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

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)))
0.4b	(/ 1 (/ (tan B) (* x 1.0)))
14.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
41×	`add-exp-log`
38×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-cbrt-cube`
16×	`div-exp`
13×	`pow-unpow`
9×	`prod-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `unpow-prod-down` `associate-r` `div-inv`
6×	`pow1` `associate-/l*`
4×	`add-log-exp`
3×	`pow-to-exp` `rec-exp` `1-exp` `associate-l` `pow-exp` `cbrt-unprod` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-/r/` `*-commutative` `inv-pow`

Counts

4 → 131

Calls

4 calls:

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)))
6.0ms	(/ 1 (/ (tan B) (* x 1.0)))
8.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series196.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
58.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
19.0ms	(/ 1 (/ (tan B) (* x 1.0)))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify87.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	799	1396
1	3765	1237
2	5001	1195

prune208.0ms

Filtered

90 candidates to 143 candidates (-58.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	143	14	157

Merged error: 0.8b

Counts

157 → 14

regimes361.0ms

Accuracy

95.7% (0.3b remaining)

Error of 1.2b against oracle of 0.9b and baseline of 8.7b

bsearch197.0ms

Steps

Iters	Range		Point
10	2.1485948544087414e+138	3.0940419388075774e+151	3.0381154039953365e+151
9	-2.378641256724455e+167	-9.381602401327605e+158	-9.621362044818768e+158

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	63
1	74	63

end0.0ms

sample9.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.321533%

Guaranteed chance to sample good point: 34.215554%

Results

1.6s	1815×	body	1280	valid
931.0ms	1545×	body	640	valid
498.0ms	3535×	body	80	valid
312.0ms	742×	body	320	valid
106.0ms	363×	body	160	valid
90.0ms	624×	body	80	invalid
13.0ms	127×	body	80	nan
1.0ms	1×	body	1280	invalid

Details

sample5.5s

simplify382.0ms

prune14.0ms

localize24.0ms

rewrite41.0ms

series134.0ms

simplify83.0ms

prune404.0ms

localize24.0ms

rewrite38.0ms

series202.0ms

simplify74.0ms

prune285.0ms

localize23.0ms

rewrite35.0ms

series202.0ms

simplify68.0ms

prune247.0ms

localize23.0ms

rewrite38.0ms

series196.0ms

simplify87.0ms

prune208.0ms

regimes361.0ms

bsearch197.0ms

simplify3.0ms

end0.0ms

sample9.0s

Profiling