Details

sample167.0ms

Algorithm

intervals

Results

44.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1509
4	498
3	162
2	74
1	37
0	18

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
0.1b	(pow (* -2 (log u1)) 0.5)
0.2b	(/ (pow (* -2 (log u1)) 0.5) 6)
0.3b	(* u2 (* 2 PI))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

65×	`unpow-prod-down`
63×	`add-sqr-sqrt`
51×	`times-frac`
46×	`*-un-lft-identity` `add-cube-cbrt`
35×	`associate-r`
21×	`associate-l`
20×	`add-exp-log`
17×	`pow1` `associate-/l*`
11×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`*-commutative`
5×	`prod-exp` `log-pow` `sqr-pow`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `cbrt-unprod`
2×	`pow-to-exp` `pow-pow`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `fma-udef` `div-inv`

Counts

4 → 166

Calls

4 calls:

0.0ms	(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
12.0ms	(pow (* -2 (log u1)) 0.5)
51.0ms	(/ (pow (* -2 (log u1)) 0.5) 6)
42.0ms	(* u2 (* 2 PI))

series2.0s

Counts

4 → 12

Calls

4 calls:

548.0ms	(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
362.0ms	(pow (* -2 (log u1)) 0.5)
1.0s	(/ (pow (* -2 (log u1)) 0.5) 6)
82.0ms	(* u2 (* 2 PI))

simplify1.7s

Counts

178 → 178

Iterations

Iter	Nodes
done	5001
2	1680
1	657
0	300

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (/ (pow (* -2 (log u1)) 0.5) 6))
0.2b	(/ (pow (* -2 (log u1)) 0.5) 6)
0.3b	(* u2 (* 2 PI))
0.4b	(expm1 (log1p (/ (pow (* -2 (log u1)) 0.5) 6)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
52×	`unpow-prod-down`
51×	`times-frac`
42×	`*-un-lft-identity` `add-cube-cbrt`
31×	`associate-r`
18×	`associate-l`
17×	`add-exp-log` `associate-/l*`
13×	`pow1`
11×	`add-cbrt-cube`
8×	`unswap-sqr`
6×	`*-commutative`
5×	`expm1-log1p-u` `log1p-expm1-u`
4×	`div-exp` `prod-exp` `log-pow` `insert-posit16` `add-log-exp` `sqr-pow`
3×	`associate-/r*` `pow-prod-down` `cbrt-unprod`
2×	`expm1-log1p` `pow-exp`
1×	`pow-to-exp` `cbrt-undiv` `log1p-udef` `clear-num` `frac-2neg` `log1p-expm1` `div-inv` `expm1-udef`

Counts

4 → 148

Calls

4 calls:

1.0ms	(log1p (/ (pow (* -2 (log u1)) 0.5) 6))
68.0ms	(/ (pow (* -2 (log u1)) 0.5) 6)
50.0ms	(* u2 (* 2 PI))
1.0ms	(expm1 (log1p (/ (pow (* -2 (log u1)) 0.5) 6)))

series3.6s

Counts

4 → 12

Calls

4 calls:

1.2s	(log1p (/ (pow (* -2 (log u1)) 0.5) 6))
1.0s	(/ (pow (* -2 (log u1)) 0.5) 6)
46.0ms	(* u2 (* 2 PI))
1.3s	(expm1 (log1p (/ (pow (* -2 (log u1)) 0.5) 6)))

simplify2.9s

Counts

160 → 160

Iterations

Iter	Nodes
done	5011
3	4632
2	1336
1	545
0	288

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2 (log u1)) (/ 0.5 2))
0.2b	(/ 6 (pow (* -2 (log u1)) (/ 0.5 2)))
0.3b	(* u2 (* 2 PI))
0.4b	(/ (pow (* -2 (log u1)) (/ 0.5 2)) (/ 6 (pow (* -2 (log u1)) (/ 0.5 2))))

rewrite367.0ms

Algorithm

rewrite-expression-head

Rules

1913×	`times-frac`
1508×	`unpow-prod-down`
1060×	`add-sqr-sqrt`
821×	`*-un-lft-identity` `add-cube-cbrt`
479×	`associate-r`
354×	`associate-l`
128×	`pow1`
120×	`unswap-sqr`
118×	`*-commutative`
116×	`log-pow` `sqr-pow`
89×	`associate-/r*`
76×	`add-exp-log`
40×	`div-exp`
23×	`associate-/r/` `associate-/l*`
22×	`pow-exp`
21×	`div-inv`
16×	`add-cbrt-cube`
14×	`prod-exp`
13×	`pow-unpow`
11×	`pow-to-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `cbrt-unprod`
2×	`pow-pow`

Counts

4 → 1230

Calls

4 calls:

15.0ms	(pow (* -2 (log u1)) (/ 0.5 2))
27.0ms	(/ 6 (pow (* -2 (log u1)) (/ 0.5 2)))
41.0ms	(* u2 (* 2 PI))
165.0ms	(/ (pow (* -2 (log u1)) (/ 0.5 2)) (/ 6 (pow (* -2 (log u1)) (/ 0.5 2))))

series2.7s

Counts

4 → 12

Calls

4 calls:

413.0ms	(pow (* -2 (log u1)) (/ 0.5 2))
1.2s	(/ 6 (pow (* -2 (log u1)) (/ 0.5 2)))
38.0ms	(* u2 (* 2 PI))
1.0s	(/ (pow (* -2 (log u1)) (/ 0.5 2)) (/ 6 (pow (* -2 (log u1)) (/ 0.5 2))))

simplify4.6s

Counts

1242 → 1242

Iterations

Iter	Nodes
done	5000
1	4497
0	1631

prune7.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b	(* u2 (* 2 PI))
0.4b	(/ (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (/ 216 (pow (* (log u1) -2) 0.5)))
0.5b	(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))
0.6b	(cbrt (/ (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (/ 216 (pow (* (log u1) -2) 0.5))))

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

16638×	`times-frac`
15228×	`unpow-prod-down`
12164×	`add-sqr-sqrt`
7591×	`*-un-lft-identity`
6685×	`add-cube-cbrt`
6543×	`associate-l`
4720×	`associate-r`
4317×	`cbrt-prod`
3644×	`unswap-sqr`
2599×	`swap-sqr`
1832×	`sqr-pow`
1438×	`pow1`
1380×	`log-pow`
1043×	`*-commutative`
359×	`add-exp-log`
164×	`prod-exp`
162×	`associate-/l*`
160×	`div-inv`
153×	`div-exp`
144×	`associate-/r*`
136×	`cbrt-div`
130×	`pow-exp`
65×	`pow-to-exp`
46×	`associate-/r/`
28×	`pow-pow` `pow-prod-down`
23×	`add-cbrt-cube`
20×	`pow-unpow`
13×	`pow-prod-up`
9×	`pow-sqr`
6×	`cbrt-undiv` `cbrt-unprod`
4×	`expm1-log1p-u` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `pow1/3`

Counts

4 → 9182

Calls

4 calls:

37.0ms	(* u2 (* 2 PI))
503.0ms	(/ (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (/ 216 (pow (* (log u1) -2) 0.5)))
140.0ms	(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))
612.0ms	(cbrt (/ (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (/ 216 (pow (* (log u1) -2) 0.5))))

series3.6s

Counts

4 → 12

Calls

4 calls:

60.0ms	(* u2 (* 2 PI))
1.5s	(/ (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (/ 216 (pow (* (log u1) -2) 0.5)))
1.0s	(* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5))
1.1s	(cbrt (/ (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (/ 216 (pow (* (log u1) -2) 0.5))))

simplify13.3s

Counts

9194 → 9194

Iterations

Iter	Nodes
done	10650
0	10650

prune1.0m

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes336.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.7s	8000×	body	80	valid
441.0ms	8000×	pre	80	true