Details

sample399.0ms

Algorithm

intervals

Results

166.0ms	64×	body	1280	valid
101.0ms	59×	body	640	valid
82.0ms	193×	body	80	valid
21.0ms	19×	body	320	valid
9.0ms	12×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	1118
2	185
1	54
0	19

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.1b

localize35.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (* (/ t l) (/ t l)) t)
3.5b	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
3.5b	(* (sin k) (* (* (/ t l) (/ t l)) t))
12.1b	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

rewrite456.0ms

Algorithm

rewrite-expression-head

Rules

209×	`add-cbrt-cube` `add-exp-log`
187×	`times-frac`
84×	`prod-exp` `cbrt-unprod`
81×	`cbrt-undiv` `div-exp`
75×	`add-sqr-sqrt`
74×	`*-un-lft-identity` `add-cube-cbrt`
35×	`associate-/l*`
28×	`associate-*l/`
25×	`associate-*r/`
23×	`associate-/r/`
18×	`pow1`
12×	`div-inv`
9×	`pow-prod-down`
7×	`frac-times`
6×	`tan-quot`
4×	`associate-/r` `associate-r` `associate-l*` `insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative` `associate-/l/`
1×	`flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 263

Calls

4 calls:

53.0ms	(* (* (/ t l) (/ t l)) t)
110.0ms	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
91.0ms	(* (sin k) (* (* (/ t l) (/ t l)) t))
191.0ms	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

series1.4s

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (* (/ t l) (/ t l)) t)
388.0ms	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
159.0ms	(* (sin k) (* (* (/ t l) (/ t l)) t))
843.0ms	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

simplify1.8s

Counts

275 → 275

Iterations

Iter	Nodes
done	5000
1	1235
0	448

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (* (/ k t) (/ k t)) 2) (tan k))
2.7b	(* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t)
4.0b	(/ (/ 2 (sin k)) (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l))))
9.4b	(* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

268×	`add-cbrt-cube` `add-exp-log`
130×	`prod-exp` `cbrt-unprod`
87×	`associate-*l/`
84×	`cbrt-undiv` `div-exp`
62×	`frac-times`
32×	`pow1`
31×	`times-frac`
30×	`tan-quot`
28×	`associate-*r/`
23×	`add-sqr-sqrt` `associate-/r/`
21×	`*-un-lft-identity` `add-cube-cbrt`
20×	`flip3-+` `flip-+`
19×	`pow-prod-down`
13×	`associate-/l*`
7×	`associate-r`
5×	`associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`*-commutative` `div-inv`
1×	`clear-num` `associate-/r*` `frac-2neg` `unswap-sqr` `associate-/l/`

Counts

4 → 244

Calls

4 calls:

35.0ms	(* (+ (* (/ k t) (/ k t)) 2) (tan k))
74.0ms	(* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t)
259.0ms	(/ (/ 2 (sin k)) (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l))))
626.0ms	(* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l)))

series1.4s

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (+ (* (/ k t) (/ k t)) 2) (tan k))
214.0ms	(* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t)
836.0ms	(/ (/ 2 (sin k)) (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l))))
251.0ms	(* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l)))

simplify2.0s

Counts

256 → 256

Iterations

Iter	Nodes
done	5001
1	1256
0	407

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.5b

localize89.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 2 t) (/ (cos k) (sin k)))
4.0b	(/ (/ 2 (sin k)) (* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (* (/ t l) (/ t l))))
5.6b	(/ (* k k) t)
9.4b	(* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (* (/ t l) (/ t l)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-cbrt-cube` `add-exp-log`
65×	`times-frac`
50×	`frac-times`
38×	`cbrt-undiv` `div-exp`
36×	`add-sqr-sqrt`
35×	`*-un-lft-identity` `add-cube-cbrt`
30×	`associate-*l/` `prod-exp` `cbrt-unprod`
26×	`associate-*r/`
24×	`frac-add` `associate-/r/`
17×	`associate-/r*`
15×	`associate-/l*`
9×	`pow1`
8×	`flip3-+` `flip-+`
7×	`div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `pow-prod-down`
1×	`associate-r` `*-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 204

Calls

4 calls:

17.0ms	(/ (* 2 t) (/ (cos k) (sin k)))
54.0ms	(/ (/ 2 (sin k)) (* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (* (/ t l) (/ t l))))
8.0ms	(/ (* k k) t)
109.0ms	(* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (* (/ t l) (/ t l)))

series1.6s

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (* 2 t) (/ (cos k) (sin k)))
939.0ms	(/ (/ 2 (sin k)) (* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (* (/ t l) (/ t l))))
21.0ms	(/ (* k k) t)
417.0ms	(* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (* (/ t l) (/ t l)))

simplify1.8s

Counts

216 → 216

Iterations

Iter	Nodes
done	5000
1	1278
0	421

prune1.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.4b

localize70.0ms

Local error

Found 4 expressions with local error:

3.3b	(* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (/ t l))
3.4b	(* (* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (/ t l)) (/ t l))
4.0b	(/ (/ 2 (sin k)) (* (* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (/ t l)) (/ t l)))
5.6b	(/ (* k k) t)

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-cbrt-cube` `add-exp-log`
57×	`frac-times` `associate-*l/`
53×	`times-frac`
40×	`add-sqr-sqrt`
39×	`cbrt-undiv` `div-exp`
35×	`*-un-lft-identity` `add-cube-cbrt`
33×	`prod-exp` `cbrt-unprod`
30×	`frac-add`
26×	`associate-r`
23×	`associate-/r/`
17×	`associate-*r/`
14×	`associate-/l*`
11×	`pow1`
10×	`flip3-+` `flip-+`
6×	`div-inv`
4×	`associate-/r` `associate-l*` `pow-prod-down` `insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative` `unswap-sqr`
1×	`associate-/l/`

Counts

4 → 215

Calls

4 calls:

84.0ms	(* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (/ t l))
100.0ms	(* (* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (/ t l)) (/ t l))
87.0ms	(/ (/ 2 (sin k)) (* (* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (/ t l)) (/ t l)))
14.0ms	(/ (* k k) t)

series1.8s

Counts

4 → 12

Calls

4 calls:

480.0ms	(* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (/ t l))
408.0ms	(* (* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (/ t l)) (/ t l))
934.0ms	(/ (/ 2 (sin k)) (* (* (+ (/ (* 2 t) (/ (cos k) (sin k))) (* (/ (* k k) t) (/ (sin k) (cos k)))) (/ t l)) (/ t l)))
21.0ms	(/ (* k k) t)

simplify2.0s

Counts

227 → 227

Iterations

Iter	Nodes
done	5001
1	1298
0	396

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.7b

regimes553.0ms

Accuracy

44.1% (3.3b remaining)

Error of 8.1b against oracle of 4.9b and baseline of 10.7b

bsearch486.0ms

Steps

Iters	Range		Point
8	1.3393316766876643e+127	8.442893536612497e+130	8.333143050057771e+130
8	-3.1240415265306656e+28	-4.3544505000805266e+24	-1.8851239965119804e+28

simplify37.0ms

Iterations

Iter	Nodes
done	76
1	76
0	57

end0.0ms

sample14.0s

Algorithm

intervals

Results

5.4s	2075×	body	1280	valid
3.1s	6010×	body	80	valid
2.9s	1684×	body	640	valid
1.4s	826×	body	320	valid
817.0ms	457×	body	160	valid