Details

analyze867.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.2%	0.1%	7
18.7%	81.2%	0.1%	8
29.7%	69.5%	0.9%	9
30.4%	67.9%	1.7%	10
36.3%	61.1%	2.6%	11
36.9%	59.5%	3.6%	12
39.9%	55.9%	4.2%	13
40.2%	54.9%	4.9%	14

sample131.0ms

Algorithm

intervals

Results

70.0ms	23×	body	2560	valid
29.0ms	49×	body	1280	valid
9.0ms	30×	body	640	valid
7.0ms	134×	body	80	valid
2.0ms	14×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	1×	body	1280	invalid
0.0ms	5×	body	80	invalid

simplify467.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	671	14
1	671	14

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 15.3b

Counts

2 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
3.7b	(/ (tan (* PI l)) (* F F))
28.7b	(tan (* PI l))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`tan-quot` `cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `associate-/l/`

Counts

4 → 66

Calls

4 calls:

3.0ms	(* PI l)
4.0ms	(* PI l)
7.0ms	(/ (tan (* PI l)) (* F F))
3.0ms	(tan (* PI l))

series42.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(* PI l)
2.0ms	(* PI l)
19.0ms	(/ (tan (* PI l)) (* F F))
17.0ms	(tan (* PI l))

simplify53.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5225	541

prune147.0ms

Filtered

53 candidates to 78 candidates (-47.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	63	15	78
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	65	15	80

Merged error: 11.1b

Counts

80 → 15

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(/ F (tan (* PI l)))
0.4b	(/ 1 (* F (/ F (tan (* PI l)))))
28.7b	(tan (* PI l))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
18×	`add-sqr-sqrt`
17×	`add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`div-exp`
9×	`pow1`
7×	`prod-exp`
6×	`associate-/l*`
5×	`cbrt-undiv`
4×	`associate-/r*` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-r` `associate-l` `cbrt-unprod`
2×	`tan-quot` `pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `div-inv`
1×	`associate-r/` `-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

4.0ms	(* PI l)
4.0ms	(/ F (tan (* PI l)))
7.0ms	(/ 1 (* F (/ F (tan (* PI l)))))
2.0ms	(tan (* PI l))

series60.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(* PI l)
27.0ms	(/ F (tan (* PI l)))
22.0ms	(/ 1 (* F (/ F (tan (* PI l)))))
8.0ms	(tan (* PI l))

simplify57.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5081	822

prune139.0ms

Filtered

63 candidates to 99 candidates (-57.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	9	5	14
Picked	1	0	1
Done	0	0	0
Total	101	13	114

Merged error: 6.9b

Counts

114 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(/ 1 (* F (+ (/ F (* PI l)) (* PI (* l (* F -1/3))))))
0.3b	(* PI (* l (* F -1/3)))
0.3b	(* F -1/3)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
22×	`add-cbrt-cube`
20×	`pow1`
15×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp`
9×	`associate-l` `pow-prod-down` `cbrt-unprod`
7×	`associate-r`
4×	`div-exp` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`cbrt-undiv` `rec-exp` `pow-flip` `1-exp` `associate-*r/` `associate-/r/` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `clear-num` `associate-/r*` `flip-+` `div-inv` `inv-pow`

Counts

4 → 87

Calls

4 calls:

4.0ms	(* PI l)
11.0ms	(/ 1 (* F (+ (/ F (* PI l)) (* PI (* l (* F -1/3))))))
7.0ms	(* PI (* l (* F -1/3)))
4.0ms	(* F -1/3)

series28.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(* PI l)
19.0ms	(/ 1 (* F (+ (/ F (* PI l)) (* PI (* l (* F -1/3))))))
5.0ms	(* PI (* l (* F -1/3)))
2.0ms	(* F -1/3)

simplify56.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5194	917

prune146.0ms

Filtered

60 candidates to 99 candidates (-65.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	96	16	112

Merged error: 6.9b

Counts

112 → 16

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* F (* (* PI l) -1/3))
0.4b	(* (* PI l) -1/3)
0.8b	(/ 1 (+ (* F (* (* PI l) -1/3)) (/ F (* PI l))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
22×	`add-cbrt-cube`
21×	`pow1`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-l`
5×	`div-inv`
4×	`associate-/r*` `distribute-lft-out` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`div-exp` `associate-/r/`
1×	`cbrt-undiv` `rec-exp` `pow-flip` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip-+` `inv-pow` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

4.0ms	(* PI l)
7.0ms	(* F (* (* PI l) -1/3))
7.0ms	(* (* PI l) -1/3)
12.0ms	(/ 1 (+ (* F (* (* PI l) -1/3)) (/ F (* PI l))))

series26.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(* PI l)
5.0ms	(* F (* (* PI l) -1/3))
3.0ms	(* (* PI l) -1/3)
16.0ms	(/ 1 (+ (* F (* (* PI l) -1/3)) (/ F (* PI l))))

simplify36.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5023	1172

prune114.0ms

Filtered

64 candidates to 106 candidates (-65.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	109	13	122

Merged error: 0.3b

Counts

122 → 13

regimes379.0ms

Accuracy

0% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	94	27
1	94	27

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.6s	841×	body	2560	valid
980.0ms	1677×	body	1280	valid
248.0ms	912×	body	640	valid
202.0ms	3947×	body	80	valid
69.0ms	396×	body	320	valid
27.0ms	227×	body	160	valid
11.0ms	191×	body	80	invalid
7.0ms	3×	body	2560	invalid
3.0ms	6×	body	1280	invalid
1.0ms	1×	body	5120	exit

Details

analyze867.0ms

sample131.0ms

simplify467.0ms

prune12.0ms

localize13.0ms

rewrite19.0ms

series42.0ms

simplify53.0ms

prune147.0ms

localize11.0ms

rewrite19.0ms

series60.0ms

simplify57.0ms

prune139.0ms

localize14.0ms

rewrite28.0ms

series28.0ms

simplify56.0ms

prune146.0ms

localize14.0ms

rewrite32.0ms

series26.0ms

simplify36.0ms

prune114.0ms

regimes379.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample4.3s

Profiling