Details

sample523.0ms

Algorithm

intervals

Results

168.0ms	30×	body	2560	valid
166.0ms	59×	body	1280	valid
23.0ms	27×	body	640	valid
21.0ms	131×	body	80	valid
8.0ms	14×	body	320	valid
5.0ms	12×	body	160	valid

simplify243.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	14
1	24	14
2	114	14
3	176	14
4	178	14
done	178	14

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.9b	(/ 1.0 (* F F))
3.9b	(* (/ 1.0 (* F F)) (tan (* PI l)))
33.2b	(tan (* PI l))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
17×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
8×	`pow1`
7×	`times-frac`
6×	`associate-r` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `associate-/l*` `unswap-sqr`
2×	`pow-prod-down` `*-commutative` `div-inv`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r*`

Counts

4 → 85

Calls

4 calls:

14.0ms	(* PI l)
16.0ms	(/ 1.0 (* F F))
104.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
18.0ms	(tan (* PI l))

series437.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* PI l)
46.0ms	(/ 1.0 (* F F))
244.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
109.0ms	(tan (* PI l))

simplify3.1s

Counts

97 → 97

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	143	924
1	1340	895
done	5001	771

prune459.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(/ F (tan (* PI l)))
0.5b	(/ 1.0 (/ F (tan (* PI l))))
33.2b	(tan (* PI l))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

87×	`times-frac`
59×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
17×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
6×	`tan-quot` `pow1` `associate-/r/` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`frac-2neg` `clear-num`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 136

Calls

4 calls:

7.0ms	(* PI l)
9.0ms	(/ F (tan (* PI l)))
39.0ms	(/ 1.0 (/ F (tan (* PI l))))
18.0ms	(tan (* PI l))

series515.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* PI l)
249.0ms	(/ F (tan (* PI l)))
160.0ms	(/ 1.0 (/ F (tan (* PI l))))
82.0ms	(tan (* PI l))

simplify3.0s

Counts

148 → 148

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	233	1903
1	1818	1817
done	5000	1723

prune711.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* 1/3 (* F (* PI l)))
0.8b	(/ 1.0 (- (/ F (* PI l)) (* 1/3 (* F (* PI l)))))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-exp-log` `add-cbrt-cube`
17×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac` `associate-l`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative` `associate-/l*`
2×	`associate-/r/` `unswap-sqr`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 94

Calls

4 calls:

13.0ms	(* PI l)
14.0ms	(* PI l)
52.0ms	(* 1/3 (* F (* PI l)))
59.0ms	(/ 1.0 (- (/ F (* PI l)) (* 1/3 (* F (* PI l)))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* PI l)
36.0ms	(* PI l)
67.0ms	(* 1/3 (* F (* PI l)))
265.0ms	(/ 1.0 (- (/ F (* PI l)) (* 1/3 (* F (* PI l)))))

simplify2.3s

Counts

106 → 106

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	146	1311
1	1333	1253
done	5000	1133

prune406.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.2b	(* PI l)
0.4b	(/ 1.0 (- (/ F (* PI l)) (* 1/3 (* F (log1p (expm1 (* PI l)))))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`times-frac` `associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `associate-/r` `-commutative` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`associate-/r/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 91

Calls

4 calls:

14.0ms	(* PI l)
15.0ms	(* PI l)
14.0ms	(* PI l)
65.0ms	(/ 1.0 (- (/ F (* PI l)) (* 1/3 (* F (log1p (expm1 (* PI l)))))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* PI l)
41.0ms	(* PI l)
33.0ms	(* PI l)
237.0ms	(/ 1.0 (- (/ F (* PI l)) (* 1/3 (* F (log1p (expm1 (* PI l)))))))

simplify2.6s

Counts

103 → 103

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	109	1217
1	1091	1094
done	5000	1008

prune496.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

regimes418.0ms

Accuracy

0% (0.4b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 0.7b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	25
1	23	25
done	23	25

end0.0ms

sample9.7s

Algorithm

intervals

Results

4.6s	816×	body	2560	valid
2.5s	1704×	body	1280	valid
1.0s	929×	body	640	valid
704.0ms	4526×	body	80	valid
249.0ms	379×	body	320	valid
104.0ms	3×	body	10240	exit
64.0ms	214×	body	160	valid