Details

sample109.0ms

Algorithm

intervals

Results

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

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 1 (63.0ms)

Iter	Nodes	Cost
0	18	19
1	35	18
2	72	18
3	156	18
4	450	18
5	1407	18
done	5000	18

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

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)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `prod-exp` `add-cbrt-cube`
12×	`pow1`
11×	`times-frac`
8×	`associate-r`
6×	`pow-exp` `add-log-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `log1p-expm1-u` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `fma-def` `flip3-+` `associate-*l/` `sum-log` `flip-+` `div-inv`

Counts

4 → 96

Calls

4 calls:

106.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
6.0ms	(pow (* -2.0 (log u1)) 0.5)
26.0ms	(* (* 2.0 PI) u2)
62.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.6s

Counts

4 → 12

Calls

4 calls:

1.0s	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
419.0ms	(pow (* -2.0 (log u1)) 0.5)
62.0ms	(* (* 2.0 PI) u2)
1.1s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.5s

Counts

108 → 108

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	211	1496
1	515	1416
2	1695	1295
done	5001	1265

prune560.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log` `add-sqr-sqrt`
33×	`associate-l`
30×	`sqrt-prod`
23×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
19×	`prod-exp`
16×	`add-cbrt-cube`
14×	`pow1`
9×	`associate-r`
7×	`cbrt-unprod`
6×	`pow-exp` `unswap-sqr`
5×	`sqrt-div` `pow-prod-down` `sqr-pow`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow` `div-inv`
1×	`frac-times` `associate-*r/`

Counts

4 → 120

Calls

4 calls:

7.0ms	(pow (* -2.0 (log u1)) 0.5)
18.0ms	(* (* 2.0 PI) u2)
118.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
39.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series2.6s

Counts

4 → 12

Calls

4 calls:

413.0ms	(pow (* -2.0 (log u1)) 0.5)
38.0ms	(* (* 2.0 PI) u2)
1.2s	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
962.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify1.9s

Counts

132 → 132

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	208	1857
1	450	1623
2	1432	1494
done	5000	1485

prune832.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.4b	(* (/ 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))
0.8b	(pow (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 3)

rewrite900.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-exp-log`
68×	`prod-exp`
40×	`add-sqr-sqrt`
38×	`add-cbrt-cube`
27×	`associate-l`
26×	`pow-exp`
24×	`add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
18×	`cbrt-unprod`
16×	`div-exp`
13×	`associate-r`
12×	`pow1`
11×	`associate-*l/`
9×	`pow-to-exp`
8×	`unswap-sqr`
7×	`sqr-pow`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`cbrt-undiv` `expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp` `rem-cube-cbrt`
3×	`unpow-prod-down` `pow-unpow` `*-commutative`
2×	`frac-times` `sub-neg` `flip3--` `pow-pow` `associate-*r/` `flip--` `div-inv`
1×	`cube-div` `cube-mult` `unpow3` `cube-prod`

Counts

4 → 166

Calls

4 calls:

23.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
39.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
757.0ms	(* (* (* (/ 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))
73.0ms	(pow (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 3)

series4.5s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (/ 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))) 0.5))
762.0ms	(pow (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 3)

simplify2.2s

Counts

178 → 178

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	304	4774
1	757	4357
2	2888	3878
done	5001	3863

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.3b	(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
0.6b	(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt 6.0))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

15.0ms	(pow (* -2.0 (log u1)) 0.5)
36.0ms	(* (* 2.0 PI) u2)
65.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
97.0ms	(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt 6.0))

series3.0s

Counts

4 → 12

Calls

4 calls:

420.0ms	(pow (* -2.0 (log u1)) 0.5)
48.0ms	(* (* 2.0 PI) u2)
1.2s	(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
1.3s	(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt 6.0))

simplify1.4s

Counts

122 → 122

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	229	1900
1	516	1728
2	1768	1579
done	5000	1570

prune695.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes743.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify14.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	25
1	27	25
done	27	25

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
752.0ms	8000×	pre	80	true