Details

sample175.0ms

Algorithm

intervals

Results

59.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
6	3468
5	1272
4	432
3	156
2	69
1	34
0	18

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-sqr-sqrt`
16×	`associate-l`
14×	`*-un-lft-identity` `add-cbrt-cube` `prod-exp` `add-cube-cbrt`
12×	`pow1`
11×	`times-frac`
6×	`associate-r` `pow-exp` `add-log-exp`
5×	`cbrt-unprod`
4×	`div-exp` `pow-prod-down` `insert-posit16` `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 → 91

Calls

4 calls:

23.0ms	(+ 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
11.0ms	(pow (* -2 (log u1)) 0.5)
26.0ms	(* u2 (* 2 PI))
57.0ms	(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))

series1.5s

Counts

4 → 12

Calls

4 calls:

481.0ms	(+ 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
393.0ms	(pow (* -2 (log u1)) 0.5)
68.0ms	(* u2 (* 2 PI))
550.0ms	(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))

simplify3.1s

Counts

103 → 103

Iterations

Iter	Nodes
3	5585
2	1563
1	506
0	205

prune650.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`pow1`
10×	`*-un-lft-identity`
9×	`prod-exp`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`add-log-exp`
5×	`div-exp`
4×	`pow-prod-down` `pow-exp` `cbrt-unprod` `insert-posit16`
3×	`pow-unpow` `associate-/r` `times-frac` `associate-l*`
2×	`pow-to-exp` `cbrt-undiv` `pow-pow`
1×	`+-commutative` `clear-num` `sum-log` `unpow-prod-down` `frac-2neg` `flip3-+` `associate-r` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

26.0ms	(+ 0.5 (/ (* (cos (* u2 (* 2 PI))) (pow (* -2 (log u1)) 0.5)) 6))
10.0ms	(pow (* -2 (log u1)) 0.5)
67.0ms	(/ (* (cos (* u2 (* 2 PI))) (pow (* -2 (log u1)) 0.5)) 6)
28.0ms	(* u2 (* 2 PI))

series1.5s

Counts

4 → 12

Calls

4 calls:

458.0ms	(+ 0.5 (/ (* (cos (* u2 (* 2 PI))) (pow (* -2 (log u1)) 0.5)) 6))
428.0ms	(pow (* -2 (log u1)) 0.5)
530.0ms	(/ (* (cos (* u2 (* 2 PI))) (pow (* -2 (log u1)) 0.5)) 6)
67.0ms	(* u2 (* 2 PI))

simplify2.4s

Counts

87 → 87

Iterations

Iter	Nodes
3	5070
2	1359
1	462
0	186

prune468.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

38×	`associate-l`
36×	`add-exp-log`
34×	`add-sqr-sqrt`
30×	`sqrt-prod`
23×	`*-un-lft-identity` `add-cube-cbrt`
21×	`add-cbrt-cube` `prod-exp`
20×	`times-frac`
16×	`pow1`
10×	`cbrt-unprod`
8×	`associate-r`
7×	`pow-prod-down`
6×	`unswap-sqr`
5×	`sqrt-div`
4×	`associate-l/` `pow-exp` `-commutative` `insert-posit16` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `div-inv`
1×	`frac-times` `unpow-prod-down` `associate-*r/`

Counts

4 → 117

Calls

4 calls:

51.0ms	(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5)))
17.0ms	(* u2 (* 2 PI))
13.0ms	(* u2 (* 2 PI))
21.0ms	(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5))

series1.3s

Counts

4 → 12

Calls

4 calls:

595.0ms	(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5)))
39.0ms	(* u2 (* 2 PI))
52.0ms	(* u2 (* 2 PI))
643.0ms	(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5))

simplify2.5s

Counts

129 → 129

Iterations

Iter	Nodes
3	5399
2	1479
1	472
0	203

prune925.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-sqr-sqrt`
14×	`-un-lft-identity` `add-cbrt-cube` `associate-r*` `prod-exp` `add-cube-cbrt`
12×	`pow1`
11×	`times-frac`
8×	`associate-l`
6×	`pow-exp` `add-log-exp`
5×	`cbrt-unprod`
4×	`div-exp` `pow-prod-down` `insert-posit16` `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-*r/` `flip-+` `div-inv`

Counts

4 → 91

Calls

4 calls:

18.0ms	(+ 0.5 (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6)))
5.0ms	(pow (* -2 (log u1)) 0.5)
13.0ms	(* u2 (* 2 PI))
21.0ms	(* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6))

series1.7s

Counts

4 → 12

Calls

4 calls:

660.0ms	(+ 0.5 (* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6)))
380.0ms	(pow (* -2 (log u1)) 0.5)
61.0ms	(* u2 (* 2 PI))
629.0ms	(* (pow (* -2 (log u1)) 0.5) (/ (cos (* u2 (* 2 PI))) 6))

simplify4.2s

Counts

103 → 103

Iterations

Iter	Nodes
3	5934
2	1759
1	525
0	208

prune528.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes275.0ms

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
2	21
1	21
0	16

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.5s	8000×	body	80	valid
380.0ms	8000×	pre	80	true