Details

sample305.0ms

Algorithm

intervals

Results

167.0ms	256×	body	80	valid
44.0ms	256×	pre	80	true

simplify3.8s

Counts: 1 → 1

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize75.0ms

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)

rewrite155.0ms

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×	`rec-exp` `1-exp` `pow-prod-down` `insert-posit16`
3×	`pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `sum-log` `flip3-+` `associate-*l/` `flip-+` `div-inv`

Counts

4 → 101

Calls

4 calls:

Slowest

80.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
34.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))
27.0ms	(* (* 2 PI) u2)
9.0ms	(pow (* -2 (log u1)) 0.5)

series2.5s

Counts

4 → 12

Calls

4 calls:

Slowest

1.6s	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))
585.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
350.0ms	(pow (* -2 (log u1)) 0.5)
56.0ms	(* (* 2 PI) u2)

simplify725.0ms

Counts: 113 → 113

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
34×	`add-exp-log`
33×	`associate-l`
32×	`sqrt-prod`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
22×	`times-frac`
19×	`prod-exp`
16×	`add-cbrt-cube`
14×	`pow1`
9×	`associate-r`
8×	`unswap-sqr`
7×	`cbrt-unprod`
6×	`pow-exp` `sqr-pow`
5×	`sqrt-div` `pow-prod-down`
4×	`associate-*l/` `insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow` `div-inv`
1×	`frac-times` `associate-*r/`

Counts

4 → 118

Calls

4 calls:

Slowest

81.0ms	(* (sqrt (/ 1 6)) (* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5)))
30.0ms	(* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5))
22.0ms	(* (* 2 PI) u2)
7.0ms	(pow (* -2 (log u1)) 0.5)

series2.7s

Counts

4 → 12

Calls

4 calls:

Slowest

1.1s	(* (sqrt (/ 1 6)) (* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5)))
1.1s	(* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5))
428.0ms	(pow (* -2 (log u1)) 0.5)
64.0ms	(* (* 2 PI) u2)

simplify2.0s

Counts: 130 → 130

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize118.0ms

Local error

Found 4 expressions with local error:

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

rewrite552.0ms

Algorithm

rewrite-expression-head

Rules

2007×	`add-exp-log`
1175×	`prod-exp`
666×	`div-exp`
266×	`pow-exp`
249×	`add-cbrt-cube`
133×	`pow-to-exp`
115×	`cbrt-unprod`
81×	`cbrt-undiv`
39×	`times-frac`
37×	`pow1`
36×	`add-sqr-sqrt`
31×	`*-un-lft-identity` `add-cube-cbrt`
21×	`associate-r`
15×	`associate-l`
14×	`swap-sqr`
13×	`associate-*r/`
10×	`div-inv`
9×	`frac-times` `associate-*l/`
8×	`pow-plus` `associate-/r/` `pow-prod-up`
6×	`frac-add`
5×	`pow3` `pow-prod-down`
4×	`pow2` `cube-unmult` `pow-sqr` `sum-cubes` `insert-posit16` `associate-/l*` `add-log-exp`
3×	`associate-/r` `flip3--` `-commutative` `flip--` `unswap-sqr`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`clear-num` `frac-2neg`

Counts

4 → 498

Calls

4 calls:

Slowest

361.0ms	(/ (+ (* (* (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6)) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6)) (* 0.5 (* 0.5 0.5))) (+ (* 0.5 (- 0.5 (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))) (* (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))))
112.0ms	(* (* (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6)) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))
28.0ms	(* (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))
26.0ms	(* (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))

series3.3s

Counts

4 → 12

Calls

4 calls:

Slowest

1.8s	(/ (+ (* (* (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6)) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6)) (* 0.5 (* 0.5 0.5))) (+ (* 0.5 (- 0.5 (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))) (* (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))))
561.0ms	(* (* (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6)) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))
505.0ms	(* (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))
460.0ms	(* (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))

simplify1.8s

Counts: 510 → 510

prune10.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize105.0ms

Local error

Found 4 expressions with local error:

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

rewrite895.0ms

Algorithm

rewrite-expression-head

Rules

4815×	`add-exp-log`
2847×	`prod-exp`
1834×	`div-exp`
630×	`pow-exp`
351×	`add-cbrt-cube`
315×	`pow-to-exp`
186×	`1-exp`
173×	`cbrt-unprod`
113×	`cbrt-undiv`
44×	`times-frac`
42×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
27×	`associate-l`
22×	`pow1`
21×	`frac-times` `associate-r` `associate-*r/`
17×	`associate-*l/`
8×	`pow-prod-down` `associate-/r/` `div-inv`
7×	`swap-sqr`
6×	`frac-add`
4×	`insert-posit16` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`associate-/r` `unpow-prod-down` `flip3--` `-commutative` `flip--` `associate-/l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`pow2` `clear-num` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up`

Counts

4 → 844

Calls

4 calls:

Slowest

505.0ms	(/ (+ (* (* (/ (cos (* (* PI u2) 2)) 1) (* (/ (pow (* -2 (log u1)) 0.5) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6)) (* 0.5 (* 0.5 0.5))) (+ (* 0.5 (- 0.5 (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))) (* (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))))
212.0ms	(* (* (/ (cos (* (* PI u2) 2)) 1) (* (/ (pow (* -2 (log u1)) 0.5) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))
48.0ms	(* (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))
34.0ms	(* (/ (pow (* -2 (log u1)) 0.5) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))

series3.4s

Counts

4 → 12

Calls

4 calls:

Slowest

1.7s	(/ (+ (* (* (/ (cos (* (* PI u2) 2)) 1) (* (/ (pow (* -2 (log u1)) 0.5) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6)) (* 0.5 (* 0.5 0.5))) (+ (* 0.5 (- 0.5 (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))) (* (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))))
584.0ms	(* (/ (pow (* -2 (log u1)) 0.5) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))
546.0ms	(* (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))
541.0ms	(* (* (/ (cos (* (* PI u2) 2)) 1) (* (/ (pow (* -2 (log u1)) 0.5) 6) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))) (/ (* (cos (* (* PI u2) 2)) (pow (* -2 (log u1)) 0.5)) 6))

simplify3.7s

Counts: 856 → 856

prune19.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes944.0ms

Accuracy

0% (0.4b remaining)

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

bsearch16.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.5s	8000×	body	80	valid
422.0ms	8000×	pre	80	true