Details

sample153.0ms

Algorithm

intervals

Results

51.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify4.1s

Counts

1 → 1

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	18	19
1	35	18
2	72	18
3	156	18
4	450	18
5	1407	18
done	5000	18

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* (/ 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))

rewrite92.0ms

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`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `associate-*l/` `fma-udef` `div-inv`

Counts

4 → 92

Calls

4 calls:

0.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
11.0ms	(pow (* -2.0 (log u1)) 0.5)
33.0ms	(* (* 2.0 PI) u2)
43.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.5s

Counts

4 → 12

Calls

4 calls:

710.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
478.0ms	(pow (* -2.0 (log u1)) 0.5)
49.0ms	(* (* 2.0 PI) u2)
1.2s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.6s

Counts

104 → 104

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	197	1340
1	447	1286
2	1439	1166
done	5000	1147

prune591.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`pow1`
9×	`prod-exp`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`div-exp`
4×	`expm1-log1p-u` `pow-prod-down` `pow-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `times-frac` `associate-r` `associate-/r*`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow`
1×	`unpow-prod-down` `frac-2neg` `associate-l` `clear-num` `-commutative` `fma-udef` `div-inv` `associate-/l` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

0.0ms	(fma (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)) 0.5)
8.0ms	(pow (* -2.0 (log u1)) 0.5)
24.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
37.0ms	(* (* 2.0 PI) u2)

series2.2s

Counts

4 → 12

Calls

4 calls:

704.0ms	(fma (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)) 0.5)
404.0ms	(pow (* -2.0 (log u1)) 0.5)
1.1s	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
48.0ms	(* (* 2.0 PI) u2)

simplify1.5s

Counts

87 → 87

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	178	1100
1	397	1053
2	1322	936
done	5000	911

prune446.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
34×	`sqrt-prod`
33×	`add-sqr-sqrt`
24×	`pow1`
21×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
18×	`times-frac`
14×	`prod-exp`
13×	`associate-r`
12×	`swap-sqr`
11×	`associate-l`
10×	`div-exp`
8×	`sqrt-pow1` `pow1/2`
6×	`pow-prod-down` `associate-/r*` `cbrt-unprod` `div-inv`
5×	`pow-prod-up`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-div` `pow-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-sqr`
2×	`pow-to-exp` `frac-2neg` `clear-num` `-commutative` `associate-/l`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `rem-square-sqrt`

Counts

4 → 138

Calls

4 calls:

30.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
32.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
38.0ms	(* (* 2.0 PI) u2)
81.0ms	(* (sqrt (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)) (sqrt (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)))

series3.5s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
980.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
44.0ms	(* (* 2.0 PI) u2)
1.2s	(* (sqrt (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)) (sqrt (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)))

simplify1.7s

Counts

150 → 150

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	205	2803
1	408	2064
2	1434	1812
done	5001	1767

prune789.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`add-exp-log`
24×	`sqrt-prod`
23×	`log-prod`
17×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r` `exp-sum`
15×	`pow1`
12×	`times-frac`
11×	`associate-l` `add-cbrt-cube`
9×	`prod-exp`
6×	`rem-log-exp` `pow-prod-down` `unswap-sqr`
5×	`div-exp`
4×	`expm1-log1p-u` `log-div` `exp-prod` `sqrt-div` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`exp-diff`
2×	`sqrt-pow1` `pow1/2` `pow-exp` `log-pow` `*-commutative`
1×	`frac-times` `pow-to-exp` `sqrt-unprod` `associate-r/` `associate-l/` `rem-exp-log`

Counts

4 → 114

Calls

4 calls:

37.0ms	(* (* 2.0 PI) u2)
11.0ms	(log (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0))
27.0ms	(exp (log (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)))
128.0ms	(* (sqrt (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)) (sqrt (exp (log (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)))))

series3.6s

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (* 2.0 PI) u2)
1.4s	(log (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0))
1.1s	(exp (log (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)))
1.1s	(* (sqrt (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)) (sqrt (exp (log (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)))))

simplify2.7s

Counts

126 → 126

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	208	2451
1	371	1977
2	1067	1618
3	3695	1556
done	5000	1547

prune874.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

Details

sample153.0ms

simplify4.1s

prune19.0ms

localize26.0ms

rewrite92.0ms

series2.5s

simplify1.6s

prune591.0ms

localize40.0ms

rewrite72.0ms

series2.2s

simplify1.5s

prune446.0ms

localize49.0ms

rewrite186.0ms

series3.5s

simplify1.7s

prune789.0ms

localize36.0ms

rewrite210.0ms

series3.6s

simplify2.7s

prune874.0ms

regimes4.0ms