Details

sample370.0ms

Algorithm

intervals

Results

123.0ms	57×	body	1280	valid
106.0ms	21×	body	2560	valid
30.0ms	43×	body	640	valid
21.0ms	147×	body	80	valid
6.0ms	12×	body	320	valid
1.0ms	3×	body	160	valid

simplify117.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.7b	(/ 1.0 (* F F))
4.3b	(* (/ 1.0 (* F F)) (tan (* PI l)))
31.3b	(tan (* PI l))

rewrite130.0ms

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` `div-exp` `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 → 77

Calls

4 calls:

7.0ms	(* PI l)
8.0ms	(/ 1.0 (* F F))
92.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
18.0ms	(tan (* PI l))

series454.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* PI l)
27.0ms	(/ 1.0 (* F F))
251.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
141.0ms	(tan (* PI l))

simplify679.0ms

Counts: 89 → 89

prune326.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
0.3b	(* (/ 1.0 F) (tan (* PI l)))
31.3b	(tan (* PI l))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`associate-l`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `times-frac`
9×	`associate-r`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`tan-quot` `pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `div-inv`

Counts

4 → 78

Calls

4 calls:

8.0ms	(* PI l)
7.0ms	(* PI l)
47.0ms	(* (/ 1.0 F) (tan (* PI l)))
8.0ms	(tan (* PI l))

series353.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* PI l)
32.0ms	(* PI l)
186.0ms	(* (/ 1.0 F) (tan (* PI l)))
101.0ms	(tan (* PI l))

simplify1.6s

Counts: 90 → 90

prune394.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 10.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(/ (sin (* PI l)) (* (cos (* PI l)) F))
30.3b	(cos (* PI l))
30.9b	(sin (* PI l))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

7.0ms	(* PI l)
21.0ms	(/ (sin (* PI l)) (* (cos (* PI l)) F))
8.0ms	(cos (* PI l))
8.0ms	(sin (* PI l))

series250.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* PI l)
149.0ms	(/ (sin (* PI l)) (* (cos (* PI l)) F))
31.0ms	(cos (* PI l))
42.0ms	(sin (* PI l))

simplify593.0ms

Counts: 65 → 65

prune366.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt l)
0.6b	(cbrt l)
30.9b	(sin (* PI l))
31.1b	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1/3`

Counts

4 → 36

Calls

4 calls:

2.0ms	(cbrt l)
2.0ms	(cbrt l)
15.0ms	(sin (* PI l))
65.0ms	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))

series666.0ms

Counts

4 → 12

Calls

4 calls:

314.0ms	(cbrt l)
279.0ms	(cbrt l)
33.0ms	(sin (* PI l))
40.0ms	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))

simplify1.1s

Counts: 48 → 48

prune279.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 6.5b

regimes629.0ms

Accuracy

85.5% (0.6b remaining)

Error of 8.3b against oracle of 7.7b and baseline of 12.1b

bsearch2.0ms

simplify942.0ms

end0.0ms

sample9.6s

Algorithm

intervals

Results

4.3s	818×	body	2560	valid
2.4s	1675×	body	1280	valid
1.1s	954×	body	640	valid
892.0ms	4617×	body	80	valid
157.0ms	365×	body	320	valid
141.0ms	4×	body	10240	exit
94.0ms	195×	body	160	valid