Details

sample377.0ms

Algorithm

intervals

Results

152.0ms	63×	body	1280	valid
74.0ms	198×	body	80	valid
72.0ms	50×	body	640	valid
39.0ms	32×	body	320	valid
17.0ms	23×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
4	2000
3	1118
2	185
1	54
0	19

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.2b

localize41.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (* (/ t l) (/ t l)) t)
3.2b	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
4.1b	(* (sin k) (* (* (/ t l) (/ t l)) t))
15.8b	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

rewrite379.0ms

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:

36.0ms	(* (* (/ t l) (/ t l)) t)
94.0ms	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
79.0ms	(* (sin k) (* (* (/ t l) (/ t l)) t))
163.0ms	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* (/ t l) (/ t l)) t)
277.0ms	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
136.0ms	(* (sin k) (* (* (/ t l) (/ t l)) t))
829.0ms	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

simplify1.5s

Counts

275 → 275

Iterations

Iter	Nodes
done	2001
2	2001
1	1235
0	448

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.9b

localize57.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (* (sin k) (* (/ t l) (/ t l))) t)
3.2b	(* (sin k) (* (/ t l) (/ t l)))
3.2b	(/ (/ 2 (tan k)) (* (* (sin k) (* (/ t l) (/ t l))) t))
15.8b	(/ (/ (/ 2 (tan k)) (* (* (sin k) (* (/ t l) (/ t l))) t)) (+ (* (/ k t) (/ k t)) 2))

rewrite416.0ms

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-*r/`
25×	`associate-*l/`
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:

111.0ms	(* (* (sin k) (* (/ t l) (/ t l))) t)
51.0ms	(* (sin k) (* (/ t l) (/ t l)))
120.0ms	(/ (/ 2 (tan k)) (* (* (sin k) (* (/ t l) (/ t l))) t))
126.0ms	(/ (/ (/ 2 (tan k)) (* (* (sin k) (* (/ t l) (/ t l))) t)) (+ (* (/ k t) (/ k t)) 2))

series1.5s

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (* (sin k) (* (/ t l) (/ t l))) t)
110.0ms	(* (sin k) (* (/ t l) (/ t l)))
318.0ms	(/ (/ 2 (tan k)) (* (* (sin k) (* (/ t l) (/ t l))) t))
949.0ms	(/ (/ (/ 2 (tan k)) (* (* (sin k) (* (/ t l) (/ t l))) t)) (+ (* (/ k t) (/ k t)) 2))

simplify1.4s

Counts

275 → 275

Iterations

Iter	Nodes
done	2010
2	2010
1	1316
0	463

prune2.2s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.6b

localize49.0ms

Local error

Found 4 expressions with local error:

9.9b	(sqrt (+ (* (/ k t) (/ k t)) 2))
9.9b	(sqrt (+ (* (/ k t) (/ k t)) 2))
10.7b	(/ (/ (/ (sqrt 2) (tan k)) t) (sqrt (+ (* (/ k t) (/ k t)) 2)))
10.8b	(* (sqrt (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (/ t l)) (/ t l)))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

1299×	`times-frac`
599×	`add-sqr-sqrt`
597×	`*-un-lft-identity` `add-cube-cbrt`
420×	`sqrt-prod`
73×	`associate-/l*`
42×	`add-cbrt-cube` `add-exp-log`
29×	`div-inv`
23×	`associate-/r/`
21×	`tan-quot`
17×	`prod-exp` `cbrt-unprod`
15×	`pow1`
14×	`sqrt-div`
12×	`associate-*r/`
11×	`cbrt-undiv` `div-exp`
9×	`frac-times`
7×	`flip3-+` `flip-+`
6×	`associate-/r` `associate-l*` `pow-prod-down`
5×	`associate-*l/`
4×	`insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`clear-num` `frac-2neg` `associate-r` `*-commutative` `associate-/l/`

Counts

4 → 613

Calls

4 calls:

28.0ms	(sqrt (+ (* (/ k t) (/ k t)) 2))
24.0ms	(sqrt (+ (* (/ k t) (/ k t)) 2))
42.0ms	(/ (/ (/ (sqrt 2) (tan k)) t) (sqrt (+ (* (/ k t) (/ k t)) 2)))
145.0ms	(* (sqrt (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (/ t l)) (/ t l)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (+ (* (/ k t) (/ k t)) 2))
73.0ms	(sqrt (+ (* (/ k t) (/ k t)) 2))
312.0ms	(/ (/ (/ (sqrt 2) (tan k)) t) (sqrt (+ (* (/ k t) (/ k t)) 2)))
241.0ms	(* (sqrt (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (/ t l)) (/ t l)))

simplify1.6s

Counts

625 → 625

Iterations

Iter	Nodes
done	2000
1	2000
0	908

prune5.4s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 12.4b

localize46.0ms

Local error

Found 4 expressions with local error:

7.0b	(* (sqrt (+ (* (/ k t) (/ k t)) 2)) (* (sin k) (/ t l)))
9.9b	(sqrt (+ (* (/ k t) (/ k t)) 2))
9.9b	(sqrt (+ (* (/ k t) (/ k t)) 2))
10.7b	(/ (/ (/ (sqrt 2) (tan k)) t) (sqrt (+ (* (/ k t) (/ k t)) 2)))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

1299×	`times-frac`
599×	`add-sqr-sqrt`
597×	`*-un-lft-identity` `add-cube-cbrt`
420×	`sqrt-prod`
73×	`associate-/l*`
29×	`div-inv`
23×	`associate-/r/`
22×	`add-cbrt-cube` `add-exp-log`
21×	`tan-quot`
11×	`pow1`
10×	`sqrt-div`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r` `associate-l*`
5×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
4×	`associate-*r/` `insert-posit16` `add-log-exp`
3×	`pow-prod-down`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/`
1×	`clear-num` `frac-2neg` `associate-r` `*-commutative` `associate-/l/`

Counts

4 → 598

Calls

4 calls:

101.0ms	(* (sqrt (+ (* (/ k t) (/ k t)) 2)) (* (sin k) (/ t l)))
26.0ms	(sqrt (+ (* (/ k t) (/ k t)) 2))
25.0ms	(sqrt (+ (* (/ k t) (/ k t)) 2))
67.0ms	(/ (/ (/ (sqrt 2) (tan k)) t) (sqrt (+ (* (/ k t) (/ k t)) 2)))

series617.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(* (sqrt (+ (* (/ k t) (/ k t)) 2)) (* (sin k) (/ t l)))
69.0ms	(sqrt (+ (* (/ k t) (/ k t)) 2))
48.0ms	(sqrt (+ (* (/ k t) (/ k t)) 2))
254.0ms	(/ (/ (/ (sqrt 2) (tan k)) t) (sqrt (+ (* (/ k t) (/ k t)) 2)))

simplify1.9s

Counts

610 → 610

Iterations

Iter	Nodes
done	2003
2	2003
1	1958
0	870

prune4.3s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 12.4b

regimes528.0ms

Accuracy

-6.8% (1.8b remaining)

Error of 13.5b against oracle of 11.7b and baseline of 13.3b

bsearch331.0ms

Steps

Iters	Range		Point
3	-4.043160302816128e-29	-2.805934415045626e-29	-2.883261033031283e-29
8	-4.3574966463759825e+39	-1.3324009274535372e+37	-2.0530128908841045e+39

simplify22.0ms

Iterations

Iter	Nodes
done	58
1	58
0	45

end0.0ms

sample14.1s

Algorithm

intervals

Results

5.8s	2088×	body	1280	valid
3.4s	1733×	body	640	valid
3.0s	5927×	body	80	valid
1.1s	851×	body	320	valid
499.0ms	430×	body	160	valid