Details

sample174.0ms

Algorithm

intervals

Results

36.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify3.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	18	628
1	34	628
2	71	628
3	155	628
4	477	628
5	3198	628
done	5000	628

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-sqr-sqrt`
14×	`-un-lft-identity` `add-cbrt-cube` `associate-l*` `prod-exp` `add-cube-cbrt`
12×	`pow1`
11×	`times-frac`
8×	`associate-r`
6×	`pow-exp` `add-log-exp`
5×	`cbrt-unprod`
4×	`div-exp` `pow-prod-down` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `sum-log` `flip3-+` `associate-*l/` `flip-+` `div-inv`

Counts

4 → 87

Calls

4 calls:

83.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
8.0ms	(pow (* -2.0 (log u1)) 0.5)
24.0ms	(* (* 2.0 PI) u2)
33.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.3s

Counts

4 → 12

Calls

4 calls:

710.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
428.0ms	(pow (* -2.0 (log u1)) 0.5)
66.0ms	(* (* 2.0 PI) u2)
1.1s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify2.3s

Counts

99 → 99

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	206	46239
1	557	43839
2	2644	43598
done	5000	43028

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize103.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.5b	(/ (- (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
0.5b	(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

666×	`add-exp-log`
500×	`prod-exp`
96×	`add-cbrt-cube`
89×	`div-exp`
88×	`pow-exp`
60×	`cbrt-unprod`
45×	`add-sqr-sqrt`
44×	`pow-to-exp`
43×	`pow1`
34×	`times-frac`
29×	`*-un-lft-identity` `add-cube-cbrt`
27×	`associate-l`
17×	`pow-prod-down`
11×	`cbrt-undiv` `associate-r` `associate-*l/`
8×	`unswap-sqr`
6×	`sqr-pow`
4×	`pow-sqr` `pow-prod-up` `associate-/l*` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `-commutative` `div-inv`
2×	`unpow-prod-down` `pow-plus` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `clear-num` `frac-2neg` `div-sub` `swap-sqr` `associate-*r/`

Counts

4 → 263

Calls

4 calls:

33.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
34.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
999.0ms	(/ (- (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
422.0ms	(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))

series3.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
974.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.1s	(/ (- (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
654.0ms	(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))

simplify2.7s

Counts

275 → 275

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	368	229232
1	1182	190990
done	5001	179667

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize96.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.4b	(* (* (* 1.0 (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))
0.5b	(/ (- (/ (* (* (* 1.0 (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) 6.0) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

rewrite976.0ms

Algorithm

rewrite-expression-head

Rules

382×	`add-exp-log`
294×	`prod-exp`
70×	`add-cbrt-cube`
52×	`pow-exp`
49×	`add-sqr-sqrt`
43×	`cbrt-unprod`
34×	`times-frac`
33×	`div-exp`
29×	`*-un-lft-identity` `add-cube-cbrt`
27×	`associate-l`
26×	`pow-to-exp`
16×	`pow1`
11×	`associate-r`
8×	`pow-prod-down` `unswap-sqr`
6×	`cbrt-undiv` `sqr-pow`
4×	`associate-l/` `associate-/l` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `-commutative` `div-inv`
2×	`unpow-prod-down` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`clear-num` `frac-2neg` `div-sub` `associate-*r/`

Counts

4 → 205

Calls

4 calls:

29.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
19.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
376.0ms	(* (* (* 1.0 (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))
541.0ms	(/ (- (/ (* (* (* 1.0 (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) 6.0) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

series4.1s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.1s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
716.0ms	(* (* (* 1.0 (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))
1.2s	(/ (- (/ (* (* (* 1.0 (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) 6.0) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

simplify3.1s

Counts

217 → 217

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	359	186861
1	1080	171374
done	5001	157851

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize143.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.4b	(/ (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
0.5b	(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))

rewrite996.0ms

Algorithm

rewrite-expression-head

Rules

1386×	`add-exp-log`
980×	`prod-exp`
269×	`div-exp`
192×	`add-cbrt-cube`
168×	`pow-exp`
116×	`cbrt-unprod`
84×	`pow-to-exp`
43×	`pow1`
38×	`add-sqr-sqrt`
35×	`cbrt-undiv`
27×	`associate-l`
25×	`times-frac`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-*l/`
17×	`pow-prod-down`
11×	`associate-r`
8×	`unswap-sqr`
6×	`sqr-pow`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`associate-/r` `-commutative` `div-inv` `associate-/l/`
2×	`frac-times` `unpow-prod-down` `pow-plus` `associate-*r/` `associate-/r/`
1×	`pow2` `clear-num` `frac-2neg` `flip3--` `swap-sqr` `flip--` `associate-/l*`

Counts

4 → 367

Calls

4 calls:

32.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
29.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
446.0ms	(/ (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
428.0ms	(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))

series4.2s

Counts

4 → 12

Calls

4 calls:

988.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.1s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.5s	(/ (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
648.0ms	(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))))

simplify3.0s

Counts

379 → 379

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	402	362132
1	1419	302783
done	5000	252621

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes1.0s

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify16.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	25	908
1	33	908
done	33	908

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
233.0ms	8000×	pre	80	true