Details

sample279.0ms

Algorithm

intervals

Results

45.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify3.3s

Counts: 1 → 1

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

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

rewrite64.0ms

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

24.0ms	(* u2 (* 2 PI))
16.0ms	(/ (pow (* -2 (log u1)) 0.5) 6)
10.0ms	(pow (* -2 (log u1)) 0.5)
0.0ms	(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)

series1.9s

Counts

4 → 12

Calls

4 calls:

Slowest

1.0s	(/ (pow (* -2 (log u1)) 0.5) 6)
516.0ms	(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
346.0ms	(pow (* -2 (log u1)) 0.5)
39.0ms	(* u2 (* 2 PI))

simplify1.8s

Counts: 105 → 105

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
72×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
52×	`add-exp-log`
26×	`div-exp`
24×	`associate-/r*`
17×	`unpow-prod-down` `sqr-pow`
16×	`add-cbrt-cube`
13×	`pow1`
10×	`pow-exp`
8×	`prod-exp`
6×	`div-inv` `associate-/l*`
5×	`pow-to-exp` `rec-exp` `1-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-l` `cbrt-unprod`
2×	`clear-num` `pow-pow` `frac-2neg`
1×	`associate-r` `associate-/r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 194

Calls

4 calls:

Slowest

26.0ms	(/ 1 (/ 6 (pow (* -2 (log u1)) 0.5)))
25.0ms	(* u2 (* 2 PI))
11.0ms	(/ 6 (pow (* -2 (log u1)) 0.5))
10.0ms	(pow (* -2 (log u1)) 0.5)

series2.5s

Counts

4 → 12

Calls

4 calls:

Slowest

1.1s	(/ 6 (pow (* -2 (log u1)) 0.5))
1.0s	(/ 1 (/ 6 (pow (* -2 (log u1)) 0.5)))
368.0ms	(pow (* -2 (log u1)) 0.5)
60.0ms	(* u2 (* 2 PI))

simplify1.1s

Counts: 206 → 206

prune2.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (pow -2 1.0) (pow (log u1) 1.0)))
0.3b	(* 6 (pow (/ 1 (* (pow -2 1.0) (pow (log u1) 1.0))) 0.5))
0.2b	(/ 1 (* 6 (pow (/ 1 (* (pow -2 1.0) (pow (log u1) 1.0))) 0.5)))
0.2b	(* u2 (* 2 PI))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

431×	`add-exp-log`
270×	`prod-exp`
214×	`pow-exp`
168×	`div-exp`
94×	`pow-to-exp`
84×	`rec-exp` `1-exp`
21×	`add-cbrt-cube`
18×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`associate-r`
11×	`pow1`
9×	`times-frac`
8×	`unpow-prod-down`
6×	`associate-l` `cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `pow-flip` `unswap-sqr`
2×	`clear-num` `associate-/r` `frac-2neg` `-commutative` `inv-pow` `sqr-pow`

Counts

4 → 264

Calls

4 calls:

Slowest

76.0ms	(* 6 (pow (/ 1 (* (pow -2 1.0) (pow (log u1) 1.0))) 0.5))
51.0ms	(/ 1 (* 6 (pow (/ 1 (* (pow -2 1.0) (pow (log u1) 1.0))) 0.5)))
29.0ms	(* u2 (* 2 PI))
14.0ms	(/ 1 (* (pow -2 1.0) (pow (log u1) 1.0)))

series3.4s

Counts

4 → 12

Calls

4 calls:

Slowest

1.2s	(/ 1 (* (pow -2 1.0) (pow (log u1) 1.0)))
1.2s	(* 6 (pow (/ 1 (* (pow -2 1.0) (pow (log u1) 1.0))) 0.5))
959.0ms	(/ 1 (* 6 (pow (/ 1 (* (pow -2 1.0) (pow (log u1) 1.0))) 0.5)))
56.0ms	(* u2 (* 2 PI))

simplify1.3s

Counts: 276 → 276

prune2.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))
0.2b	(* (* 2 PI) u2)
0.1b	(pow (* -2 (log u1)) 0.5)
0.0b	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
25×	`add-sqr-sqrt`
24×	`prod-exp`
16×	`*-un-lft-identity`
14×	`add-cbrt-cube` `associate-l` `add-cube-cbrt`
13×	`times-frac`
12×	`pow1`
10×	`pow-exp`
8×	`div-exp` `associate-r`
6×	`add-log-exp` `unswap-sqr`
5×	`pow-to-exp` `cbrt-unprod` `sqr-pow`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `pow-prod-down` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `sum-log` `fma-def` `flip3-+` `associate-*l/` `flip-+` `div-inv`

Counts

4 → 110

Calls

4 calls:

Slowest

73.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
31.0ms	(* (* 2 PI) u2)
18.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))
5.0ms	(pow (* -2 (log u1)) 0.5)

series2.0s

Counts

4 → 12

Calls

4 calls:

Slowest

871.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))
686.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
423.0ms	(pow (* -2 (log u1)) 0.5)
35.0ms	(* (* 2 PI) u2)

simplify855.0ms

Counts: 122 → 122

prune1.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes754.0ms

Accuracy

0% (0.3b remaining)

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

bsearch10.0ms

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
362.0ms	8000×	pre	80	true