Details

analyze1.9s

Algorithm: search

sample126.0ms

Algorithm

intervals

Results

56.0ms	60×	body	1280	valid
25.0ms	41×	body	640	valid
19.0ms	129×	body	80	valid
6.0ms	14×	body	320	valid
3.0ms	12×	body	160	valid
3.0ms	17×	body	80	invalid
0.0ms	1×	body	80	nan

simplify389.0ms

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

prune13.0ms

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: 15.1b

Counts

2 → 1

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.2b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
16.7b	(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)))
13.0ms	(* (/ 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)))

series132.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (tan B))
25.0ms	(* x (/ 1.0 (tan B)))
64.0ms	(* (/ 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)))

simplify87.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (68.0ms)

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

prune391.0ms

Filtered

128 candidates to 167 candidates (-30.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	151	16	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	152	16	168

Merged error: 1.1b

Counts

168 → 16

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.3b	(* x (/ 1.0 (tan B)))
16.7b	(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:

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

series198.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
57.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
23.0ms	(* x (/ 1.0 (tan B)))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (15.0ms)

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

prune276.0ms

Filtered

90 candidates to 120 candidates (-33.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	10	5	15
Picked	1	0	1
Done	0	0	0
Total	121	15	136

Merged error: 1.1b

Counts

136 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
16.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite34.0ms

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))

series198.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (* x 1.0) (tan B))
95.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
59.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
21.0ms	(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

prune238.0ms

Filtered

82 candidates to 109 candidates (-32.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	109	15	124

Merged error: 1.1b

Counts

124 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.3b	(* x (/ 1.0 (sin B)))
16.7b	(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`
20×	`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×	`pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r`

Counts

4 → 107

Calls

4 calls:

9.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
12.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
6.0ms	(* x (/ 1.0 (sin B)))
8.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series187.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
59.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
11.0ms	(* x (/ 1.0 (sin B)))
21.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	685	1163
1	3084	1041
2	5002	1041

prune203.0ms

Filtered

92 candidates to 119 candidates (-29.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	119	15	134

Merged error: 1.1b

Counts

134 → 15

regimes345.0ms

Accuracy

97.9% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 10.6b

bsearch2.2s

Steps

Iters	Range		Point
9	1.2560072864182311e+154	1.5643179096053713e+160	1.3567353650491317e+154
9	-6.248882605991208e+162	-4.428791215040906e+153	-1.3599240956164297e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	64
1	76	64

end0.0ms

analyze1.6s

Algorithm: search

sample3.6s

Algorithm

intervals

Results

1.5s	1652×	body	1280	valid
854.0ms	1449×	body	640	valid
523.0ms	3834×	body	80	valid
308.0ms	730×	body	320	valid
94.0ms	676×	body	80	invalid
91.0ms	335×	body	160	valid
14.0ms	118×	body	80	nan

Details

analyze1.9s

sample126.0ms

simplify389.0ms

prune13.0ms

localize47.0ms

rewrite41.0ms

series132.0ms

simplify87.0ms

prune391.0ms

localize21.0ms

rewrite38.0ms

series198.0ms

simplify76.0ms

prune276.0ms

localize22.0ms

rewrite34.0ms

series198.0ms

simplify68.0ms

prune238.0ms

localize22.0ms

rewrite38.0ms

series187.0ms

simplify75.0ms

prune203.0ms

regimes345.0ms

bsearch2.2s

simplify2.0ms

end0.0ms

analyze1.6s

sample3.6s

Profiling