Details

sample222.0ms

Algorithm

intervals

Results

89.0ms	256×	body	80	valid
17.0ms	256×	pre	80	true

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	990
3	206
2	74
1	36
0	18

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 0.5 (* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6))
0.2b	(pow (* -2 (log u1)) 0.5)
0.3b	(* PI u2)
0.4b	(* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
12×	`prod-exp`
11×	`pow1` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `add-log-exp`
4×	`associate-l` `pow-exp` `cbrt-unprod` `insert-posit16`
3×	`pow-unpow` `pow-prod-down`
2×	`pow-to-exp` `pow-pow` `*-commutative`
1×	`+-commutative` `sum-log` `unpow-prod-down` `flip3-+` `flip-+` `unswap-sqr` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

22.0ms	(+ 0.5 (* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6))
5.0ms	(pow (* -2 (log u1)) 0.5)
5.0ms	(* PI u2)
80.0ms	(* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6)

series1.4s

Counts

4 → 12

Calls

4 calls:

513.0ms	(+ 0.5 (* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6))
371.0ms	(pow (* -2 (log u1)) 0.5)
39.0ms	(* PI u2)
511.0ms	(* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6)

simplify1.9s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	1837
1	453
0	171

prune485.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* -2 (log u1)) 0.5)
0.3b	(* (* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) (sqrt 1/6)) (sqrt 1/6))
0.3b	(* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) (sqrt 1/6))
0.3b	(* PI u2)

rewrite357.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
28×	`prod-exp`
20×	`add-cbrt-cube`
16×	`pow1`
15×	`associate-r`
13×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`cbrt-unprod`
6×	`pow-prod-down` `pow-exp` `sqrt-prod`
5×	`associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`pow-pow`
1×	`unpow-prod-down` `unswap-sqr` `sqr-pow`

Counts

4 → 88

Calls

4 calls:

10.0ms	(pow (* -2 (log u1)) 0.5)
197.0ms	(* (* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) (sqrt 1/6)) (sqrt 1/6))
138.0ms	(* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) (sqrt 1/6))
10.0ms	(* PI u2)

series1.4s

Counts

4 → 12

Calls

4 calls:

403.0ms	(pow (* -2 (log u1)) 0.5)
513.0ms	(* (* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) (sqrt 1/6)) (sqrt 1/6))
464.0ms	(* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) (sqrt 1/6))
28.0ms	(* PI u2)

simplify1.8s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	2434
1	485
0	179

prune606.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (+ 0.5 (* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6)))
0.3b	(* PI u2)
0.3b	(exp (log (+ 0.5 (* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6))))
0.4b	(* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6)

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
12×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `prod-exp`
10×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`log-prod` `associate-r`
4×	`log-div` `exp-prod` `associate-l` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`exp-sum`
2×	`flip3-+` `exp-diff` `pow-prod-down` `pow-exp` `log-pow` `*-commutative` `flip-+`
1×	`pow-to-exp` `rem-log-exp` `unswap-sqr` `rem-exp-log`

Counts

4 → 73

Calls

4 calls:

3.0ms	(log (+ 0.5 (* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6)))
5.0ms	(* PI u2)
4.0ms	(exp (log (+ 0.5 (* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6))))
91.0ms	(* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6)

series1.6s

Counts

4 → 12

Calls

4 calls:

545.0ms	(log (+ 0.5 (* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6)))
33.0ms	(* PI u2)
515.0ms	(exp (log (+ 0.5 (* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6))))
492.0ms	(* (* (cos (* 2 (* PI u2))) (pow (* -2 (log u1)) 0.5)) 1/6)

simplify1.6s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
2	1615
1	421
0	188

prune670.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6))
0.4b	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6))
0.5b	(* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6)))
0.6b	(cbrt (* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

422×	`add-exp-log`
361×	`prod-exp`
80×	`pow-exp`
50×	`add-cbrt-cube`
40×	`pow-to-exp`
33×	`cbrt-unprod`
11×	`pow1` `associate-l`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r` `*-commutative`
2×	`unpow-prod-down` `sqr-pow`
1×	`cbrt-prod` `pow2` `pow-plus` `pow1/3` `swap-sqr` `pow3` `pow-prod-down` `pow-sqr` `pow-prod-up` `rem-cbrt-cube`

Counts

4 → 168

Calls

4 calls:

74.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6))
59.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6))
355.0ms	(* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6)))
728.0ms	(cbrt (* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6))))

series2.4s

Counts

4 → 12

Calls

4 calls:

539.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6))
563.0ms	(* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6))
666.0ms	(* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6)))
594.0ms	(cbrt (* (* (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6)) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6))) (* (pow (* -2 (log u1)) 0.5) (* (cos (* (* u2 PI) 2)) 1/6))))

simplify2.3s

Counts

180 → 180

Iterations

Iter	Nodes
done	5000
2	2806
1	644
0	204

prune892.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes531.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	35
1	35
0	25

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.7s	8000×	body	80	valid
422.0ms	8000×	pre	80	true