Details

sample318.0ms

Algorithm

intervals

Results

156.0ms	66×	body	1280	valid
58.0ms	45×	body	640	valid
49.0ms	182×	body	80	valid
26.0ms	28×	body	320	valid
10.0ms	17×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
4	6637
3	1079
2	183
1	52
0	19

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.0b

localize41.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (tan k) (fma (/ k t) (/ k t) 2))
1.5b	(/ t (* (/ l t) (/ l t)))
3.2b	(* (/ t (* (/ l t) (/ l t))) (sin k))
17.8b	(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

141×	`add-cbrt-cube` `add-exp-log`
66×	`cbrt-undiv` `div-exp`
43×	`prod-exp` `cbrt-unprod`
21×	`add-sqr-sqrt` `times-frac`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-l`
11×	`associate-/l*`
9×	`associate-/r/`
8×	`pow1`
7×	`associate-*l/`
6×	`associate-r`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `tan-quot` `associate-r/` `*-commutative` `fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-/l/`

Counts

4 → 157

Calls

4 calls:

15.0ms	(* (tan k) (fma (/ k t) (/ k t) 2))
15.0ms	(/ t (* (/ l t) (/ l t)))
36.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
52.0ms	(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (tan k) (fma (/ k t) (/ k t) 2))
54.0ms	(/ t (* (/ l t) (/ l t)))
97.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
299.0ms	(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

simplify1.4s

Counts

169 → 169

Iterations

Iter	Nodes
2	3731
1	852
0	299

prune2.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2 (* t (sin k)))
1.2b	(* (tan k) (fma (/ k t) (/ k t) 2))
5.9b	(/ (/ 2 (* t (sin k))) (/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t))))
14.4b	(/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

244×	`add-cbrt-cube` `add-exp-log`
129×	`cbrt-undiv` `div-exp`
95×	`times-frac`
65×	`prod-exp` `cbrt-unprod`
36×	`add-sqr-sqrt`
34×	`*-un-lft-identity` `add-cube-cbrt`
28×	`associate-/r/`
20×	`div-inv`
11×	`associate-l/` `associate-/l`
10×	`associate-/r*`
9×	`frac-times` `associate-*r/`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `associate-l`
2×	`tan-quot` `fma-udef` `associate-/l/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 236

Calls

4 calls:

16.0ms	(/ 2 (* t (sin k)))
17.0ms	(* (tan k) (fma (/ k t) (/ k t) 2))
45.0ms	(/ (/ 2 (* t (sin k))) (/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t))))
33.0ms	(/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t)))

series904.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ 2 (* t (sin k)))
136.0ms	(* (tan k) (fma (/ k t) (/ k t) 2))
483.0ms	(/ (/ 2 (* t (sin k))) (/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t))))
197.0ms	(/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t)))

simplify2.4s

Counts

248 → 248

Iterations

Iter	Nodes
2	5388
1	1170
0	404

prune3.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.4b

localize79.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ k l) (/ k l))
1.1b	(* (/ (sin k) (cos k)) (* (/ k l) (/ k l)))
2.7b	(* (/ (sin k) (cos k)) (* (/ t l) (/ t l)))
5.9b	(/ (/ 2 (* t (sin k))) (fma (* (/ (sin k) (cos k)) (* (/ t l) (/ t l))) 2 (* (/ (sin k) (cos k)) (* (/ k l) (/ k l)))))

rewrite502.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-cbrt-cube` `add-exp-log`
93×	`times-frac`
80×	`add-sqr-sqrt`
62×	`*-un-lft-identity` `add-cube-cbrt`
41×	`prod-exp` `cbrt-unprod`
39×	`associate-l`
35×	`cbrt-undiv` `div-exp`
21×	`pow1`
15×	`associate-r`
13×	`swap-sqr`
11×	`frac-times` `associate-*r/` `div-inv`
8×	`unswap-sqr`
7×	`pow-prod-down` `associate-l/` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative`
1×	`pow2` `clear-num` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up` `associate-/l/`

Counts

4 → 229

Calls

4 calls:

23.0ms	(* (/ k l) (/ k l))
411.0ms	(* (/ (sin k) (cos k)) (* (/ k l) (/ k l)))
31.0ms	(* (/ (sin k) (cos k)) (* (/ t l) (/ t l)))
33.0ms	(/ (/ 2 (* t (sin k))) (fma (* (/ (sin k) (cos k)) (* (/ t l) (/ t l))) 2 (* (/ (sin k) (cos k)) (* (/ k l) (/ k l)))))

series942.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (/ k l) (/ k l))
132.0ms	(* (/ (sin k) (cos k)) (* (/ k l) (/ k l)))
177.0ms	(* (/ (sin k) (cos k)) (* (/ t l) (/ t l)))
586.0ms	(/ (/ 2 (* t (sin k))) (fma (* (/ (sin k) (cos k)) (* (/ t l) (/ t l))) 2 (* (/ (sin k) (cos k)) (* (/ k l) (/ k l)))))

simplify1.5s

Counts

241 → 241

Iterations

Iter	Nodes
2	4565
1	1254
0	416

prune3.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.6b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ k l) (/ k l))
1.0b	(* (sin k) (* (/ k l) (/ k l)))
2.7b	(* (/ (sin k) (cos k)) (* (/ t l) (/ t l)))
5.9b	(/ (/ 2 (* t (sin k))) (fma (* (/ (sin k) (cos k)) (* (/ t l) (/ t l))) 2 (/ (* (sin k) (* (/ k l) (/ k l))) (cos k))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-cbrt-cube` `add-exp-log`
83×	`times-frac`
72×	`add-sqr-sqrt`
56×	`*-un-lft-identity` `add-cube-cbrt`
32×	`prod-exp` `cbrt-unprod`
29×	`associate-l`
26×	`cbrt-undiv` `div-exp`
21×	`pow1`
15×	`associate-r`
13×	`swap-sqr`
10×	`associate-*r/` `div-inv`
7×	`frac-times` `pow-prod-down` `associate-/l*` `unswap-sqr`
5×	`associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative`
1×	`pow2` `clear-num` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up` `associate-/l/`

Counts

4 → 204

Calls

4 calls:

12.0ms	(* (/ k l) (/ k l))
38.0ms	(* (sin k) (* (/ k l) (/ k l)))
30.0ms	(* (/ (sin k) (cos k)) (* (/ t l) (/ t l)))
26.0ms	(/ (/ 2 (* t (sin k))) (fma (* (/ (sin k) (cos k)) (* (/ t l) (/ t l))) 2 (/ (* (sin k) (* (/ k l) (/ k l))) (cos k))))

series883.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (/ k l) (/ k l))
73.0ms	(* (sin k) (* (/ k l) (/ k l)))
139.0ms	(* (/ (sin k) (cos k)) (* (/ t l) (/ t l)))
643.0ms	(/ (/ 2 (* t (sin k))) (fma (* (/ (sin k) (cos k)) (* (/ t l) (/ t l))) 2 (/ (* (sin k) (* (/ k l) (/ k l))) (cos k))))

simplify1.3s

Counts

216 → 216

Iterations

Iter	Nodes
2	4016
1	1152
0	395

prune3.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.6b

regimes473.0ms

Accuracy

65.1% (1.7b remaining)

Error of 5.0b against oracle of 3.3b and baseline of 8.3b

bsearch307.0ms

Steps

Iters	Range		Point
6	2.2017224295722193e-141	1.6729163369772663e-140	1.6490058462058476e-140
7	-5.246887493406821e-56	-1.6674163510033618e-57	-3.313813655101207e-57

simplify16.0ms

Iterations

Iter	Nodes
2	44
1	44
0	39

end0.0ms

sample15.7s

Algorithm

intervals

Results

6.7s	2101×	body	1280	valid
3.5s	5900×	body	80	valid
3.5s	1765×	body	640	valid
1.2s	841×	body	320	valid
318.0ms	405×	body	160	valid