Details

sample123.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify1.1s

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize90.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `prod-exp` `add-cbrt-cube`
12×	`pow1`
11×	`times-frac`
8×	`associate-r`
6×	`pow-exp` `add-log-exp`
5×	`cbrt-unprod`
4×	`div-exp` `pow-prod-down` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-*l/` `sum-log` `flip-+` `div-inv`

Counts

4 → 87

Calls

4 calls:

95.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
13.0ms	(pow (* -2.0 (log u1)) 0.5)
28.0ms	(* (* 2.0 PI) u2)
30.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.3s

Counts

4 → 12

Calls

4 calls:

739.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
372.0ms	(pow (* -2.0 (log u1)) 0.5)
61.0ms	(* (* 2.0 PI) u2)
1.2s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.1s

Counts: 99 → 99

prune461.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.3b	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
12×	`pow1`
11×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`unpow-prod-down` `prod-exp` `associate-/l*` `sqr-pow`
4×	`div-exp` `pow-prod-down` `pow-exp`
3×	`pow-unpow` `associate-r` `associate-/r*` `cbrt-unprod`
2×	`pow-to-exp` `pow-pow`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `associate-l` `clear-num` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 84

Calls

4 calls:

95.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
12.0ms	(pow (* -2.0 (log u1)) 0.5)
23.0ms	(* (* 2.0 PI) u2)
9.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series2.2s

Counts

4 → 12

Calls

4 calls:

685.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
443.0ms	(pow (* -2.0 (log u1)) 0.5)
67.0ms	(* (* 2.0 PI) u2)
1.0s	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify932.0ms

Counts: 96 → 96

prune528.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
0.3b	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
0.4b	(/ (- (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))
0.5b	(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

330×	`add-exp-log`
219×	`prod-exp`
118×	`pow1`
90×	`add-cbrt-cube`
66×	`pow-prod-down`
65×	`div-exp`
56×	`cbrt-unprod`
42×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`pow-exp`
16×	`pow-to-exp`
14×	`associate-/l*`
11×	`cbrt-undiv`
9×	`associate-/r*` `pow-sqr` `pow-prod-up`
8×	`unpow-prod-down` `sqr-pow`
5×	`associate-r/` `associate-l/`
4×	`add-log-exp` `difference-of-squares`
3×	`frac-2neg` `pow-plus` `clear-num` `div-inv`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `div-sub` `swap-sqr` `associate-r` `associate-l` `*-commutative`

Counts

4 → 222

Calls

4 calls:

18.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
18.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
1.1s	(/ (- (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))
482.0ms	(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))

series4.6s

Counts

4 → 12

Calls

4 calls:

1.5s	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
1.2s	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
1.2s	(/ (- (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))
702.0ms	(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))

simplify2.3s

Counts: 234 → 234

prune997.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))))
0.5b	(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))
0.5b	(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))
0.5b	(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))

rewrite5.8s

Algorithm

rewrite-expression-head

Rules

31828×	`add-exp-log`
24851×	`prod-exp`
9347×	`pow1`
5768×	`div-exp`
5543×	`pow-prod-down`
2998×	`add-cbrt-cube`
2884×	`pow-exp`
2361×	`cbrt-unprod`
1442×	`pow-to-exp`
1439×	`pow-prod-up`
1073×	`pow-sqr`
296×	`cbrt-undiv`
295×	`pow-plus`
58×	`associate-r/` `associate-l/`
52×	`pow2`
20×	`frac-times`
4×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `swap-sqr` `associate-r` `associate-l` `-commutative` `add-log-exp`
1×	`unswap-sqr`

Counts

4 → 4393

Calls

4 calls:

2.8s	(* (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))))
434.0ms	(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))
482.0ms	(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))
430.0ms	(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))

series2.7s

Counts

4 → 12

Calls

4 calls:

644.0ms	(* (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))))
689.0ms	(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))
654.0ms	(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))
734.0ms	(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))

simplify6.1s

Counts: 4405 → 4405

prune5.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes645.0ms

Accuracy

17.3% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.3s

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
177.0ms	8000×	pre	80	true