Details

sample135.0ms

Algorithm

intervals

Results

49.0ms	256×	body	80	valid
14.0ms	256×	pre	80	true

simplify526.0ms

Calls

1 calls:

Slowest

525.0ms

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
0.3b	(* u2 (* 2 PI))
0.1b	(pow (* -2 (log u1)) 0.5)
0.0b	(+ 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
40×	`associate-r`
32×	`add-exp-log`
30×	`unpow-prod-down`
29×	`*-un-lft-identity`
26×	`associate-l`
25×	`add-cube-cbrt`
16×	`pow1` `unswap-sqr`
14×	`add-cbrt-cube` `prod-exp`
13×	`times-frac`
9×	`associate-*l/`
6×	`pow-exp` `add-log-exp`
5×	`pow-prod-down` `*-commutative` `cbrt-unprod`
4×	`div-exp` `insert-posit16` `sqr-pow`
3×	`pow-to-exp` `pow-unpow` `associate-/r` `associate-/l`
2×	`pow-pow` `log-pow` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `flip-+` `div-inv`

Calls

4 calls:

Slowest

97.0ms	(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
60.0ms	(+ 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
20.0ms	(* u2 (* 2 PI))
8.0ms	(pow (* -2 (log u1)) 0.5)

series1.3s

Calls

4 calls:

Slowest

448.0ms	(+ 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
419.0ms	(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
367.0ms	(pow (* -2 (log u1)) 0.5)
33.0ms	(* u2 (* 2 PI))

simplify20.7s

Calls

120 calls:

Slowest

835.0ms	(+ (* 1/6 (* (pow (* (pow (log (/ 1 u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) (cos (* 2 (* u2 PI))))) 0.5)
818.0ms	(* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))
792.0ms	(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* (sqrt -2) (sqrt (log u1))) 0.5))
783.0ms	(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* (sqrt -2) (sqrt (log u1))) 0.5))
746.0ms	(* (/ (sqrt (cos (* u2 (* 2 PI)))) (sqrt 6)) (pow (sqrt (* -2 (log u1))) 0.5))

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite447.0ms

Algorithm

rewrite-expression-head

Rules

300×	`add-sqr-sqrt`
189×	`sqrt-div`
124×	`unswap-sqr`
122×	`associate-r`
108×	`associate-*l/`
105×	`sqrt-prod`
87×	`*-un-lft-identity` `add-cube-cbrt`
81×	`frac-times`
66×	`associate-l`
63×	`associate-/r` `associate-/l`
60×	`times-frac`
56×	`unpow-prod-down`
36×	`add-exp-log`
23×	`pow1`
21×	`clear-num` `frac-2neg` `add-cbrt-cube` `prod-exp`
17×	`sqr-pow`
10×	`pow-prod-down` `cbrt-unprod`
9×	`associate-r/` `-commutative`
4×	`pow-exp` `insert-posit16` `add-log-exp`
3×	`div-inv`
2×	`pow-to-exp` `log-pow`

Calls

4 calls:

Slowest

304.0ms	(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5)))
64.0ms	(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5))
35.0ms	(* u2 (* 2 PI))
34.0ms	(* u2 (* 2 PI))

series1.1s

Calls

4 calls:

Slowest

532.0ms	(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5))
491.0ms	(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* -2 (log u1)) 0.5)))
44.0ms	(* u2 (* 2 PI))
34.0ms	(* u2 (* 2 PI))

simplify1.8m

Calls

457 calls:

Slowest

1.1s	(* (sqrt (/ (cos (* u2 (* 2 PI))) (cbrt 6))) (pow (* -2 (log u1)) 0.5))
1.0s	(* (sqrt (/ (sqrt (cos (* u2 (* 2 PI)))) (sqrt 6))) (pow (* -2 (log u1)) (/ 0.5 2)))
836.0ms	(* (sqrt (sqrt (/ (cos (* u2 (* 2 PI))) 6))) (pow (sqrt (* -2 (log u1))) 0.5))
818.0ms	(* (pow (* (pow (log (/ 1 u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) (* (sqrt 1/6) (sqrt (cos (* 2 (* u2 PI))))))
799.0ms	(* (sqrt (sqrt (/ (cos (* u2 (* 2 PI))) 6))) (pow (sqrt (* -2 (log u1))) 0.5))

prune5.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (* (* (sqrt (/ (cos (* (* PI 2) u2)) 6)) (pow (* -2 (log u1)) 0.5)) (sqrt (cos (* (* PI 2) u2)))) (sqrt 6))
0.3b	(* (sqrt (/ (cos (* (* PI 2) u2)) 6)) (pow (* -2 (log u1)) 0.5))
0.3b	(* (* PI 2) u2)
0.3b	(* (* PI 2) u2)

rewrite537.0ms

Algorithm

rewrite-expression-head

Rules

1158×	`add-sqr-sqrt`
682×	`times-frac`
656×	`sqrt-prod`
532×	`associate-l`
528×	`unswap-sqr`
316×	`*-un-lft-identity` `add-cube-cbrt`
236×	`unpow-prod-down`
222×	`associate-r`
93×	`associate-/l*`
74×	`sqr-pow`
43×	`add-exp-log`
27×	`associate-l/` `-commutative`
25×	`add-cbrt-cube`
24×	`pow1`
21×	`prod-exp`
18×	`sqrt-div`
12×	`associate-/r*`
10×	`cbrt-unprod`
9×	`div-inv` `associate-/l/`
8×	`log-pow`
7×	`pow-prod-down`
6×	`div-exp`
4×	`pow-exp` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `clear-num` `frac-2neg`
2×	`pow-to-exp`

Calls

4 calls:

Slowest

380.0ms	(/ (* (* (sqrt (/ (cos (* (* PI 2) u2)) 6)) (pow (* -2 (log u1)) 0.5)) (sqrt (cos (* (* PI 2) u2)))) (sqrt 6))
67.0ms	(* (sqrt (/ (cos (* (* PI 2) u2)) 6)) (pow (* -2 (log u1)) 0.5))
22.0ms	(* (* PI 2) u2)
21.0ms	(* (* PI 2) u2)

series1.3s

Calls

4 calls:

Slowest

678.0ms	(/ (* (* (sqrt (/ (cos (* (* PI 2) u2)) 6)) (pow (* -2 (log u1)) 0.5)) (sqrt (cos (* (* PI 2) u2)))) (sqrt 6))
548.0ms	(* (sqrt (/ (cos (* (* PI 2) u2)) 6)) (pow (* -2 (log u1)) 0.5))
53.0ms	(* (* PI 2) u2)
43.0ms	(* (* PI 2) u2)