Details

sample188.0ms

Algorithm

intervals

Results

61.0ms	256×	body	80	valid
14.0ms	256×	pre	80	true

simplify3.6s

Counts: 1 → 1

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

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:

Slowest

28.0ms	(* u2 (* 2 PI))
18.0ms	(/ (pow (* -2 (log u1)) 0.5) 6)
11.0ms	(pow (* -2 (log u1)) 0.5)
0.0ms	(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)

series2.1s

Counts

4 → 12

Calls

4 calls:

Slowest

1.1s	(/ (pow (* -2 (log u1)) 0.5) 6)
560.0ms	(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
391.0ms	(pow (* -2 (log u1)) 0.5)
60.0ms	(* u2 (* 2 PI))

simplify1.5s

Counts: 105 → 105

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

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:

Slowest

18.0ms	(* u2 (* 2 PI))
13.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
6.0ms	(pow (* -2 (log u1)) 0.5)
0.0ms	(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)

series2.4s

Counts

4 → 12

Calls

4 calls:

Slowest

1.4s	(* (pow (* -2 (log u1)) 0.5) 1/6)
502.0ms	(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)
378.0ms	(pow (* -2 (log u1)) 0.5)
34.0ms	(* u2 (* 2 PI))

simplify1.4s

Counts: 90 → 90

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
36×	`add-sqr-sqrt`
34×	`times-frac`
33×	`prod-exp`
25×	`*-un-lft-identity` `add-cube-cbrt`
20×	`div-exp` `associate-r` `pow-exp`
16×	`add-cbrt-cube`
13×	`sqr-pow`
10×	`pow-to-exp`
9×	`pow1`
8×	`unpow-prod-down` `associate-l`
6×	`unswap-sqr`
5×	`cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `pow-prod-down`
2×	`cbrt-undiv` `*-commutative` `div-inv`
1×	`clear-num` `frac-2neg` `associate-*r/` `fma-udef`

Counts

4 → 137

Calls

4 calls:

Slowest

19.0ms	(* u2 (* 2 PI))
18.0ms	(* (pow (* -2 (log u1)) (/ 0.5 2)) (/ (pow (* -2 (log u1)) (/ 0.5 2)) 6))
8.0ms	(/ (pow (* -2 (log u1)) (/ 0.5 2)) 6)
0.0ms	(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) (/ 0.5 2)) (/ (pow (* -2 (log u1)) (/ 0.5 2)) 6)) 0.5)

series2.5s

Counts

4 → 12

Calls

4 calls:

Slowest

1.0s	(* (pow (* -2 (log u1)) (/ 0.5 2)) (/ (pow (* -2 (log u1)) (/ 0.5 2)) 6))
932.0ms	(/ (pow (* -2 (log u1)) (/ 0.5 2)) 6)
515.0ms	(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) (/ 0.5 2)) (/ (pow (* -2 (log u1)) (/ 0.5 2)) 6)) 0.5)
68.0ms	(* u2 (* 2 PI))

simplify997.0ms

Counts: 149 → 149

prune2.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b	(expm1 (log1p (/ (pow (* -2 (log u1)) 0.5) 6)))
0.3b	(/ (pow (* -2 (log u1)) 0.5) 6)
0.2b	(* u2 (* 2 PI))
0.2b	(log1p (/ (pow (* -2 (log u1)) 0.5) 6))

rewrite27.0ms

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:

Slowest

17.0ms	(* u2 (* 2 PI))
8.0ms	(/ (pow (* -2 (log u1)) 0.5) 6)
0.0ms	(log1p (/ (pow (* -2 (log u1)) 0.5) 6))
0.0ms	(expm1 (log1p (/ (pow (* -2 (log u1)) 0.5) 6)))

series3.6s

Counts

4 → 12

Calls

4 calls:

Slowest

1.3s	(expm1 (log1p (/ (pow (* -2 (log u1)) 0.5) 6)))
1.2s	(log1p (/ (pow (* -2 (log u1)) 0.5) 6))
1.0s	(/ (pow (* -2 (log u1)) 0.5) 6)
54.0ms	(* u2 (* 2 PI))

simplify1.0s

Counts: 98 → 98

prune1.4s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0b

regimes318.0ms

Accuracy

0% (0.3b remaining)

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

bsearch6.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.2s	8000×	body	80	valid
837.0ms	8000×	pre	80	true