Details

sample463.0ms

Algorithm

intervals

Results

94.0ms	23×	body	2560	valid
27.0ms	39×	body	1280	valid
16.0ms	45×	body	640	valid
11.0ms	141×	body	80	valid
3.0ms	14×	body	320	valid
1.0ms	7×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	7
1	39	7
2	76	7
3	114	7
4	137	7
5	144	7
6	144	7
done	144	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.7b	(/ 1.0 (* F F))
3.9b	(* (/ 1.0 (* F F)) (tan (* PI l)))
30.2b	(tan (* PI l))

rewrite75.0ms

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))
47.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
9.0ms	(tan (* PI l))

series265.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* PI l)
25.0ms	(/ 1.0 (* F F))
136.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
77.0ms	(tan (* PI l))

simplify41.0ms

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	323	443
1	1416	374
2	5001	374
done	5001	374

prune221.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (/ (cbrt 1.0) F) (tan (* PI l)))
30.2b	(tan (* PI l))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

7.0ms	(* PI l)
7.0ms	(* PI l)
37.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
8.0ms	(tan (* PI l))

series276.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
24.0ms	(* PI l)
165.0ms	(* (/ (cbrt 1.0) F) (tan (* PI l)))
66.0ms	(tan (* PI l))

simplify91.0ms

Counts

100 → 100

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	294	496
1	1023	455
2	3911	454
3	5001	451
done	5001	451

prune323.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.3b	(/ (* (cbrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
29.6b	(cos (* PI l))
29.9b	(sin (* PI l))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

7.0ms	(* PI l)
25.0ms	(/ (* (cbrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
7.0ms	(cos (* PI l))
7.0ms	(sin (* PI l))

series262.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
198.0ms	(/ (* (cbrt 1.0) (sin (* PI l))) (* F (cos (* PI l))))
17.0ms	(cos (* PI l))
26.0ms	(sin (* PI l))

simplify43.0ms

Counts

65 → 65

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	341	430
1	1637	341
2	5001	341
done	5001	341

prune238.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt l)
0.5b	(cbrt l)
29.8b	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))
29.9b	(sin (* PI l))

rewrite47.0ms

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:

1.0ms	(cbrt l)
1.0ms	(cbrt l)
38.0ms	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))
7.0ms	(sin (* PI l))

series411.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt l)
178.0ms	(cbrt l)
28.0ms	(cos (* (* PI (* (cbrt l) (cbrt l))) (cbrt l)))
26.0ms	(sin (* PI l))

simplify87.0ms

Counts

48 → 48

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	148	217
1	491	191
2	2191	187
3	5002	182
done	5002	182

prune203.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.0b

regimes381.0ms

Accuracy

86.8% (0.6b remaining)

Error of 8.1b against oracle of 7.5b and baseline of 12.2b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	57
1	70	57
done	70	57

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.5s	807×	body	2560	valid
1.2s	1663×	body	1280	valid
336.0ms	983×	body	640	valid
309.0ms	4537×	body	80	valid
139.0ms	6×	body	10240	exit
89.0ms	404×	body	320	valid
29.0ms	190×	body	160	valid