Details

sample268.0ms

Algorithm

intervals

Results

106.0ms	59×	body	1280	valid
61.0ms	54×	body	640	valid
39.0ms	177×	body	80	valid
26.0ms	34×	body	320	valid
7.0ms	12×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	903
2	161
1	48
0	19

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.9b

localize53.0ms

Local error

Found 4 expressions with local error:

1.7b	(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
5.8b	(/ (pow t 3.0) l)
10.6b	(/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k)))
15.9b	(* (/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k))) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

614×	`times-frac`
245×	`add-sqr-sqrt`
240×	`*-un-lft-identity` `add-cube-cbrt`
157×	`add-exp-log`
94×	`add-cbrt-cube`
93×	`unpow-prod-down`
90×	`associate-/l*`
87×	`div-exp`
85×	`associate-l`
45×	`cbrt-undiv`
37×	`prod-exp`
31×	`sqr-pow`
23×	`cbrt-unprod`
17×	`div-inv`
13×	`associate-r`
7×	`pow-to-exp` `associate-/r*` `pow-exp`
6×	`pow1`
5×	`associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`tan-quot` `unswap-sqr`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 417

Calls

4 calls:

6.0ms	(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
7.0ms	(/ (pow t 3.0) l)
42.0ms	(/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k)))
168.0ms	(* (/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k))) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series2.0s

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
243.0ms	(/ (pow t 3.0) l)
625.0ms	(/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k)))
1.0s	(* (/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k))) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify2.6s

Counts

429 → 429

Iterations

Iter	Nodes
done	5000
1	2324
0	752

prune4.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 18.5b

localize147.0ms

Local error

Found 4 expressions with local error:

3.4b	(* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))
5.1b	(/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k))
6.3b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
10.0b	(* (/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k)) (* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0)))))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

4481×	`times-frac`
2027×	`add-sqr-sqrt`
1829×	`*-un-lft-identity` `add-cube-cbrt`
1353×	`associate-l`
1246×	`add-exp-log`
888×	`cbrt-prod`
783×	`sqrt-prod`
746×	`div-exp`
708×	`unpow-prod-down`
377×	`prod-exp`
321×	`add-cbrt-cube`
188×	`cbrt-undiv`
160×	`sqr-pow`
104×	`cbrt-unprod`
84×	`pow-exp`
75×	`div-inv`
64×	`associate-/l*`
54×	`pow-to-exp`
40×	`unswap-sqr`
14×	`associate-r`
11×	`pow1` `associate-/r/`
6×	`frac-times` `associate-*r/`
4×	`expm1-log1p-u` `associate-/r` `pow-prod-down` `associate-l/` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`tan-quot` `associate-/l/`

Counts

4 → 1947

Calls

4 calls:

729.0ms	(* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))
38.0ms	(/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k))
11.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
633.0ms	(* (/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k)) (* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0)))))

series3.6s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))
587.0ms	(/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k))
339.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
1.3s	(* (/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k)) (* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0)))))

simplify4.1s

Counts

1959 → 1959

Iterations

Iter	Nodes
done	5000
0	2005

prune26.4s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 11.4b

localize218.0ms

Local error

Found 4 expressions with local error:

1.7b	(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
3.4b	(* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))
3.7b	(* (/ (/ (sqrt (* (cbrt 2.0) (cbrt 2.0))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (cbrt (sin k)) (cbrt (sin k)))) (* (/ (/ (sqrt (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))))
4.0b	(* (/ (/ (sqrt (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0)))))

rewrite5.6s

Algorithm

rewrite-expression-head

Rules

13777×	`add-exp-log`
9262×	`times-frac`
8461×	`div-exp`
4576×	`prod-exp`
3959×	`add-sqr-sqrt`
3761×	`*-un-lft-identity` `add-cube-cbrt`
3303×	`cbrt-prod`
3187×	`associate-l`
1985×	`add-cbrt-cube`
1852×	`sqrt-prod`
1405×	`cbrt-undiv`
1012×	`unpow-prod-down`
930×	`pow-exp`
922×	`cbrt-unprod`
564×	`pow-to-exp`
464×	`sqr-pow`
91×	`div-inv`
40×	`unswap-sqr`
23×	`frac-times` `associate-*r/`
20×	`pow1`
15×	`associate-r`
11×	`associate-*l/` `associate-/r/`
10×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative` `associate-/l*`
1×	`clear-num` `frac-2neg` `tan-quot`

Counts

4 → 4934

Calls

4 calls:

14.0ms	(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
720.0ms	(* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))
2.3s	(* (/ (/ (sqrt (* (cbrt 2.0) (cbrt 2.0))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (cbrt (sin k)) (cbrt (sin k)))) (* (/ (/ (sqrt (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))))
1.2s	(* (/ (/ (sqrt (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0)))))

series3.3s

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
887.0ms	(* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))
1.3s	(* (/ (/ (sqrt (* (cbrt 2.0) (cbrt 2.0))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (cbrt (sin k)) (cbrt (sin k)))) (* (/ (/ (sqrt (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))))
977.0ms	(* (/ (/ (sqrt (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (cbrt (sin k))) (* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0)))))

simplify8.7s

Counts

4946 → 4946

Iterations

Iter	Nodes
done	5001
0	3857

prune1.2m

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 10.7b

localize318.0ms

Local error

Found 4 expressions with local error:

5.3b	(* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (* (/ (cbrt l) (cbrt (fma 2 1.0 (pow (/ k t) 2.0)))) (/ (cbrt l) (cbrt (fma 2 1.0 (pow (/ k t) 2.0))))))
16.7b	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
16.7b	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
16.7b	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

3452×	`times-frac`
1555×	`add-sqr-sqrt`
1486×	`*-un-lft-identity` `add-cube-cbrt`
1172×	`associate-l`
885×	`cbrt-prod`
656×	`unpow-prod-down`
585×	`sqrt-prod`
167×	`add-exp-log`
112×	`sqr-pow`
84×	`div-exp`
69×	`add-cbrt-cube`
54×	`prod-exp`
46×	`cbrt-undiv`
36×	`cbrt-unprod`
22×	`div-inv`
20×	`unswap-sqr`
9×	`pow1`
5×	`frac-times` `pow-to-exp` `pow-exp` `associate-*r/`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `pow-prod-down` `associate-*l/`
1×	`associate-r` `tan-quot` `*-commutative`

Counts

4 → 1301

Calls

4 calls:

1.0s	(* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (* (/ (cbrt l) (cbrt (fma 2 1.0 (pow (/ k t) 2.0)))) (/ (cbrt l) (cbrt (fma 2 1.0 (pow (/ k t) 2.0))))))
1.0ms	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
1.0ms	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
1.0ms	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

766.0ms	(* (/ (/ (sqrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) (* (/ (cbrt l) (cbrt (fma 2 1.0 (pow (/ k t) 2.0)))) (/ (cbrt l) (cbrt (fma 2 1.0 (pow (/ k t) 2.0))))))
157.0ms	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
204.0ms	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
209.0ms	(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))

simplify4.0s

Counts

1313 → 1313

Iterations

Iter	Nodes
done	5001
1	3975
0	1176

prune23.1s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 10.6b

regimes1.3s

Accuracy

0% (1.1b remaining)

Error of 12.3b against oracle of 11.2b and baseline of 12.3b

bsearch0.0ms

simplify22.0ms

Iterations

Iter	Nodes
done	48
1	48
0	43

end0.0ms

sample10.3s

Algorithm

intervals

Results

4.4s	2042×	body	1280	valid
2.4s	1721×	body	640	valid
2.1s	5963×	body	80	valid
667.0ms	848×	body	320	valid
193.0ms	437×	body	160	valid