Details

sample435.0ms

Algorithm

intervals

Results

256.0ms	256×	body	80	valid
17.0ms	256×	pre	80	true

simplify4.2s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

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))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
16×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
15×	`times-frac`
12×	`pow1`
11×	`add-cbrt-cube`
5×	`unpow-prod-down` `prod-exp` `associate-/l*` `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` `associate-l*` `cbrt-unprod`
2×	`pow-to-exp` `pow-pow`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-r` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 93

Calls

4 calls:

0.0ms	(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
5.0ms	(pow (* -2 (log u1)) 0.5)
7.0ms	(/ (pow (* -2 (log u1)) 0.5) 6)
34.0ms	(* u2 (* 2 PI))

series2.0s

Counts

4 → 12

Calls

4 calls:

506.0ms	(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
410.0ms	(pow (* -2 (log u1)) 0.5)
994.0ms	(/ (pow (* -2 (log u1)) 0.5) 6)
65.0ms	(* u2 (* 2 PI))

simplify2.8s

Counts

105 → 105

Iterations

Iter	Nodes
done	5088
3	4506
2	1192
1	417
0	189

prune571.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)
0.1b	(pow (* -2 (log u1)) 0.5)
0.3b	(* u2 (* 2 PI))
0.3b	(* (pow (* -2 (log u1)) 0.5) 1/6)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
12×	`pow1`
11×	`add-sqr-sqrt` `add-cbrt-cube`
9×	`prod-exp`
8×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `pow-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `pow-pow` `*-commutative` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 78

Calls

4 calls:

0.0ms	(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)
5.0ms	(pow (* -2 (log u1)) 0.5)
13.0ms	(* u2 (* 2 PI))
16.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)

series2.0s

Counts

4 → 12

Calls

4 calls:

500.0ms	(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)
411.0ms	(pow (* -2 (log u1)) 0.5)
67.0ms	(* u2 (* 2 PI))
999.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)

simplify3.1s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
3	4101
2	1102
1	382
0	160

prune495.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize43.0ms

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))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

209×	`times-frac`
96×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
76×	`add-exp-log`
43×	`unpow-prod-down` `sqr-pow`
40×	`div-exp`
24×	`associate-/r*`
22×	`pow-exp`
16×	`add-cbrt-cube`
14×	`prod-exp`
13×	`pow-unpow`
12×	`pow1`
11×	`pow-to-exp`
9×	`div-inv`
8×	`associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `cbrt-unprod`
2×	`clear-num` `pow-pow` `frac-2neg`
1×	`associate-r` `associate-/r/` `*-commutative`

Counts

4 → 247

Calls

4 calls:

6.0ms	(pow (* -2 (log u1)) (/ 0.5 2))
6.0ms	(/ 6 (pow (* -2 (log u1)) (/ 0.5 2)))
33.0ms	(* u2 (* 2 PI))
27.0ms	(/ (pow (* -2 (log u1)) (/ 0.5 2)) (/ 6 (pow (* -2 (log u1)) (/ 0.5 2))))

series2.6s

Counts

4 → 12

Calls

4 calls:

381.0ms	(pow (* -2 (log u1)) (/ 0.5 2))
1.1s	(/ 6 (pow (* -2 (log u1)) (/ 0.5 2)))
63.0ms	(* u2 (* 2 PI))
1.0s	(/ (pow (* -2 (log u1)) (/ 0.5 2)) (/ 6 (pow (* -2 (log u1)) (/ 0.5 2))))

simplify2.7s

Counts

259 → 259

Iterations

Iter	Nodes
done	5003
2	3737
1	1093
0	420

prune1.8s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize47.0ms

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)))

rewrite459.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

1.0ms	(log1p (/ (pow (* -2 (log u1)) 0.5) 6))
14.0ms	(/ (pow (* -2 (log u1)) 0.5) 6)
29.0ms	(* u2 (* 2 PI))
413.0ms	(expm1 (log1p (/ (pow (* -2 (log u1)) 0.5) 6)))

series3.4s

Counts

4 → 12

Calls

4 calls:

1.2s	(log1p (/ (pow (* -2 (log u1)) 0.5) 6))
926.0ms	(/ (pow (* -2 (log u1)) 0.5) 6)
67.0ms	(* u2 (* 2 PI))
1.2s	(expm1 (log1p (/ (pow (* -2 (log u1)) 0.5) 6)))

simplify2.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5008
3	2842
2	893
1	343
0	177

prune657.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0b

regimes357.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.7s	8000×	body	80	valid
381.0ms	8000×	pre	80	true