Details

sample129.0ms

Algorithm

intervals

Results

72.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify481.0ms

Calls

1 calls:

Slowest

480.0ms

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

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite214.0ms

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

96.0ms	(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
73.0ms	(+ 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
26.0ms	(* u2 (* 2 PI))
13.0ms	(pow (* -2 (log u1)) 0.5)

series1.4s

Calls

4 calls:

Slowest

508.0ms	(+ 0.5 (* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5)))
472.0ms	(* (/ (cos (* u2 (* 2 PI))) 6) (pow (* -2 (log u1)) 0.5))
399.0ms	(pow (* -2 (log u1)) 0.5)
33.0ms	(* u2 (* 2 PI))

simplify21.4s

Calls

120 calls:

Slowest

1.1s	(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* (sqrt -2) (sqrt (log u1))) 0.5))
928.0ms	(* 1/6 (* (cos (* 2 (* u2 PI))) (pow (* (pow -1 1.0) (* (pow -2 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)))
866.0ms	(+ (* 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)
740.0ms	(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (sqrt (* -2 (log u1))) 0.5))
721.0ms	(* (sqrt (/ (cos (* u2 (* 2 PI))) 6)) (pow (* (sqrt -2) (sqrt (log u1))) 0.5))

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

383×	`times-frac`
233×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
196×	`add-cube-cbrt`
195×	`unpow-prod-down`
66×	`associate-l`
60×	`associate-r`
32×	`add-exp-log`
27×	`pow1`
20×	`associate-/l*`
19×	`div-inv` `unswap-sqr`
17×	`*-commutative`
16×	`associate-/r*`
15×	`log-pow` `sqr-pow`
14×	`add-cbrt-cube`
12×	`div-exp`
9×	`associate-/r/`
6×	`pow-exp` `prod-exp` `add-log-exp`
4×	`pow-prod-down` `insert-posit16`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `cbrt-unprod`
2×	`clear-num` `pow-pow` `frac-2neg`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`

Calls

4 calls:

Slowest

80.0ms	(+ 0.5 (/ (pow (* (log u1) -2) 0.5) (/ 6 (cos (* u2 (* 2 PI))))))
45.0ms	(/ (pow (* (log u1) -2) 0.5) (/ 6 (cos (* u2 (* 2 PI)))))
36.0ms	(* u2 (* 2 PI))
12.0ms	(pow (* (log u1) -2) 0.5)

series1.8s

Calls

4 calls:

Slowest

681.0ms	(+ 0.5 (/ (pow (* (log u1) -2) 0.5) (/ 6 (cos (* u2 (* 2 PI))))))
646.0ms	(/ (pow (* (log u1) -2) 0.5) (/ 6 (cos (* u2 (* 2 PI)))))
367.0ms	(pow (* (log u1) -2) 0.5)
59.0ms	(* u2 (* 2 PI))

simplify2.4m

Calls

544 calls:

Slowest

905.0ms	(+ (* 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)
874.0ms	(/ (pow (* (log u1) 1) 0.5) (/ (* (cbrt 6) (cbrt 6)) (sqrt (cos (* u2 (* 2 PI))))))
814.0ms	(/ (pow (* (cbrt (* (log u1) -2)) (cbrt (* (log u1) -2))) 0.5) (/ 1 (* (cbrt (cos (* u2 (* 2 PI)))) (cbrt (cos (* u2 (* 2 PI)))))))
787.0ms	(/ (pow (* (log u1) (sqrt -2)) 0.5) (/ (* (cbrt 6) (cbrt 6)) (sqrt (cos (* u2 (* 2 PI))))))
775.0ms	(/ (pow (* (sqrt (log u1)) (sqrt -2)) 0.5) (/ (* (cbrt 6) (cbrt 6)) (sqrt (cos (* u2 (* 2 PI))))))

prune4.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

2563×	`times-frac`
1266×	`add-sqr-sqrt`
1125×	`*-un-lft-identity`
1123×	`add-cube-cbrt`
884×	`unpow-prod-down`
278×	`associate-l`
265×	`associate-/r*`
219×	`associate-r`
104×	`add-exp-log`
93×	`div-inv`
81×	`pow1`
72×	`unswap-sqr`
70×	`*-commutative`
68×	`log-pow` `sqr-pow`
66×	`div-exp`
42×	`associate-/r/`
37×	`associate-/l*`
23×	`add-cbrt-cube`
20×	`associate-/l/`
18×	`pow-exp`
12×	`prod-exp`
9×	`pow-to-exp` `cbrt-undiv` `rec-exp` `1-exp`
7×	`clear-num`
5×	`frac-2neg`
4×	`pow-prod-down` `insert-posit16` `remove-double-div` `add-log-exp`
3×	`pow-unpow` `cbrt-unprod`
2×	`pow-pow`
1×	`pow-flip` `inv-pow`

Calls

4 calls:

Slowest

103.0ms	(/ 1 (/ (/ 6 (cos (* u2 (* 2 PI)))) (pow (* (log u1) -2) 0.5)))
55.0ms	(/ (/ 6 (cos (* u2 (* 2 PI)))) (pow (* (log u1) -2) 0.5))
22.0ms	(* u2 (* 2 PI))
9.0ms	(pow (* (log u1) -2) 0.5)

series1.6s

Calls

4 calls:

Slowest

597.0ms	(/ (/ 6 (cos (* u2 (* 2 PI)))) (pow (* (log u1) -2) 0.5))
577.0ms	(/ 1 (/ (/ 6 (cos (* u2 (* 2 PI)))) (pow (* (log u1) -2) 0.5)))
363.0ms	(pow (* (log u1) -2) 0.5)
53.0ms	(* u2 (* 2 PI))