Details

sample128.0ms

Algorithm

intervals

Results

41.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
6	3778
5	1307
4	450
3	160
2	72
1	35
0	18

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
0.1b	(pow (* -2 (log u1)) 0.5)
0.3b	(* u2 (* 2 PI))
0.3b	(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite75.0ms

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` `add-cube-cbrt`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `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))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
10.0ms	(pow (* -2 (log u1)) 0.5)
27.0ms	(* u2 (* 2 PI))
34.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.0s

Counts

4 → 12

Calls

4 calls:

538.0ms	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
402.0ms	(pow (* -2 (log u1)) 0.5)
45.0ms	(* u2 (* 2 PI))
1.1s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.3s

Counts

90 → 90

Iterations

Iter	Nodes
3	3303
2	970
1	350
0	159

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2 (log u1)) 0.5)
0.2b	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
0.3b	(* u2 (* 2 PI))
0.3b	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
19×	`prod-exp`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
15×	`associate-l`
14×	`pow1`
11×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-prod`
7×	`associate-r` `cbrt-unprod`
6×	`pow-exp`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow`

Counts

4 → 98

Calls

4 calls:

5.0ms	(pow (* -2 (log u1)) 0.5)
45.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
19.0ms	(* u2 (* 2 PI))
16.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series2.7s

Counts

4 → 12

Calls

4 calls:

417.0ms	(pow (* -2 (log u1)) 0.5)
1.1s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
62.0ms	(* u2 (* 2 PI))
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify1.6s

Counts

110 → 110

Iterations

Iter	Nodes
3	3224
2	1079
1	360
0	159

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
13×	`add-sqr-sqrt`
11×	`pow1` `add-cbrt-cube`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`prod-exp`
6×	`log-prod` `associate-r` `associate-l`
4×	`expm1-log1p-u` `exp-prod` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum` `pow-prod-down`
2×	`pow-exp` `log-pow` `*-commutative` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `unpow-prod-down` `rem-log-exp` `rem-exp-log`

Counts

4 → 80

Calls

4 calls:

1.0ms	(log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5))
33.0ms	(* u2 (* 2 PI))
18.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
3.0ms	(exp (log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)))

series2.3s

Counts

4 → 12

Calls

4 calls:

626.0ms	(log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5))
59.0ms	(* u2 (* 2 PI))
1.1s	(* 1/6 (pow (* -2 (log u1)) 0.5))
495.0ms	(exp (log (fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)))

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
3	3307
2	973
1	371
0	180

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-exp-log`
69×	`prod-exp`
34×	`pow-exp`
22×	`add-sqr-sqrt`
17×	`pow-to-exp` `*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube`
14×	`pow1`
13×	`pow-unpow`
11×	`associate-l`
9×	`times-frac` `sqr-pow`
7×	`associate-r` `cbrt-unprod`
6×	`pow-prod-down`
5×	`unpow-prod-down` `swap-sqr` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-pow`
1×	`pow2` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 138

Calls

4 calls:

12.0ms	(pow (* -2 (log u1)) (/ 0.5 2))
27.0ms	(* u2 (* 2 PI))
44.0ms	(* 1/6 (* (pow (* -2 (log u1)) (/ 0.5 2)) (pow (* -2 (log u1)) (/ 0.5 2))))
31.0ms	(* (pow (* -2 (log u1)) (/ 0.5 2)) (pow (* -2 (log u1)) (/ 0.5 2)))

series2.9s

Counts

4 → 12

Calls

4 calls:

807.0ms	(pow (* -2 (log u1)) (/ 0.5 2))
49.0ms	(* u2 (* 2 PI))
1.0s	(* 1/6 (* (pow (* -2 (log u1)) (/ 0.5 2)) (pow (* -2 (log u1)) (/ 0.5 2))))
1.0s	(* (pow (* -2 (log u1)) (/ 0.5 2)) (pow (* -2 (log u1)) (/ 0.5 2)))

simplify4.0s

Counts

150 → 150

Iterations

Iter	Nodes
3	5242
2	1585
1	585
0	223

prune2.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes380.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
2	22
1	22
0	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.2s	8000×	body	80	valid
420.0ms	8000×	pre	80	true