Details

sample228.0ms

Algorithm

intervals

Results

117.0ms	78×	body	1280	valid
47.0ms	59×	body	640	valid
29.0ms	190×	body	80	valid
12.0ms	23×	body	320	valid
4.0ms	10×	body	160	valid

simplify1.7s

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: 22.9b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (/ t l) (/ t l)) t)
2.4b	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
3.1b	(* (sin k) (* (* (/ t l) (/ t l)) t))
17.0b	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

rewrite585.0ms

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:

70.0ms	(* (* (/ t l) (/ t l)) t)
130.0ms	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
166.0ms	(* (sin k) (* (* (/ t l) (/ t l)) t))
207.0ms	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (* (/ t l) (/ t l)) t)
358.0ms	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
138.0ms	(* (sin k) (* (* (/ t l) (/ t l)) t))
799.0ms	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

simplify2.1s

Counts

275 → 275

Iterations

Iter	Nodes
done	5000
1	1235
0	448

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ t l) (/ t l))
2.6b	(* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t)
2.8b	(/ (/ 2 (sin k)) (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l))))
16.8b	(* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l)))

rewrite961.0ms

Algorithm

rewrite-expression-head

Rules

278×	`add-cbrt-cube` `add-exp-log`
133×	`prod-exp` `cbrt-unprod`
88×	`cbrt-undiv` `div-exp`
86×	`associate-*l/`
71×	`times-frac`
61×	`frac-times`
59×	`add-sqr-sqrt`
47×	`*-un-lft-identity` `add-cube-cbrt`
37×	`pow1`
28×	`associate-*r/`
27×	`tan-quot`
23×	`associate-/r/`
19×	`pow-prod-down`
18×	`flip3-+` `flip-+`
17×	`associate-r`
15×	`associate-l`
13×	`swap-sqr` `associate-/l*`
7×	`div-inv`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up` `associate-/l/`

Counts

4 → 288

Calls

4 calls:

30.0ms	(* (/ t l) (/ t l))
116.0ms	(* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t)
365.0ms	(/ (/ 2 (sin k)) (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l))))
419.0ms	(* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l)))

series1.4s

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (/ t l) (/ t l))
178.0ms	(* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t)
940.0ms	(/ (/ 2 (sin k)) (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l))))
276.0ms	(* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l)))

simplify2.1s

Counts

300 → 300

Iterations

Iter	Nodes
done	5002
1	1526
0	455

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.9b

localize33.0ms

Local error

Found 4 expressions with local error:

2.6b	(* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t)
2.8b	(/ (/ 2 (sin k)) (* (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (/ t l)) (/ t l)))
7.9b	(* (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (/ t l)) (/ t l))
10.8b	(* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (/ t l))

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

272×	`add-cbrt-cube` `add-exp-log`
129×	`prod-exp` `cbrt-unprod`
124×	`associate-*l/`
87×	`cbrt-undiv` `div-exp`
69×	`frac-times`
49×	`times-frac`
33×	`add-sqr-sqrt` `*-un-lft-identity` `tan-quot` `add-cube-cbrt`
32×	`pow1`
29×	`associate-r`
23×	`associate-/r/`
22×	`flip3-+` `flip-+`
19×	`pow-prod-down`
18×	`associate-*r/`
13×	`associate-/l*`
5×	`div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`associate-l` `*-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `associate-/l/`

Counts

4 → 273

Calls

4 calls:

92.0ms	(* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t)
1.2s	(/ (/ 2 (sin k)) (* (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (/ t l)) (/ t l)))
1.1s	(* (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (/ t l)) (/ t l))
315.0ms	(* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (/ t l))

series1.6s

Counts

4 → 12

Calls

4 calls:

207.0ms	(* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t)
857.0ms	(/ (/ 2 (sin k)) (* (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (/ t l)) (/ t l)))
266.0ms	(* (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (/ t l)) (/ t l))
253.0ms	(* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (/ t l))

simplify2.2s

Counts

285 → 285

Iterations

Iter	Nodes
done	5000
1	1460
0	444

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.4b

localize88.0ms

Local error

Found 4 expressions with local error:

3.9b	(* (/ (* t t) l) (/ (sin k) (cos k)))
7.0b	(/ (* t t) l)
7.9b	(* (+ (* (/ (sin k) (cos k)) (/ (* k k) l)) (* 2 (* (/ (* t t) l) (/ (sin k) (cos k))))) (/ t l))
10.5b	(/ (* k k) l)

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
32×	`times-frac` `associate-*r/`
26×	`associate-r`
25×	`*-un-lft-identity` `add-cube-cbrt`
24×	`frac-times` `associate-*l/`
18×	`frac-add`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
10×	`associate-l`
8×	`pow1`
6×	`associate-/r*` `unswap-sqr`
5×	`div-inv`
4×	`insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `flip3-+` `pow-prod-down` `-commutative` `flip-+` `associate-/l`

Counts

4 → 148

Calls

4 calls:

52.0ms	(* (/ (* t t) l) (/ (sin k) (cos k)))
10.0ms	(/ (* t t) l)
117.0ms	(* (+ (* (/ (sin k) (cos k)) (/ (* k k) l)) (* 2 (* (/ (* t t) l) (/ (sin k) (cos k))))) (/ t l))
11.0ms	(/ (* k k) l)

series608.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (/ (* t t) l) (/ (sin k) (cos k)))
21.0ms	(/ (* t t) l)
403.0ms	(* (+ (* (/ (sin k) (cos k)) (/ (* k k) l)) (* 2 (* (/ (* t t) l) (/ (sin k) (cos k))))) (/ t l))
26.0ms	(/ (* k k) l)

simplify2.8s

Counts

160 → 160

Iterations

Iter	Nodes
done	5000
2	4902
1	1054
0	324

prune1.2s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 3.9b

regimes631.0ms

Accuracy

56% (4.1b remaining)

Error of 7.3b against oracle of 3.2b and baseline of 12.6b

bsearch467.0ms

Steps

Iters	Range		Point
8	1.9361814694442347e+157	4.230872522382776e+160	1.9659319169181852e+157
9	-7.223268975160798e+166	-2.350382245908277e+159	-2.7347896894361278e+159

simplify18.0ms

Iterations

Iter	Nodes
done	67
1	67
0	45

end0.0ms

sample10.4s

Algorithm

intervals

Results

3.7s	2045×	body	1280	valid
2.8s	5941×	body	80	valid
2.1s	1744×	body	640	valid
718.0ms	851×	body	320	valid
645.0ms	410×	body	160	valid