Details

sample206.0ms

Algorithm

intervals

Results

51.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify4.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1408
4	387
3	148
2	72
1	35
0	18

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (cos (* 2.0 (* PI u2))) (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* PI u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
25×	`add-sqr-sqrt`
16×	`associate-l`
15×	`*-un-lft-identity` `add-cube-cbrt`
12×	`prod-exp`
11×	`times-frac` `add-cbrt-cube`
9×	`pow1`
8×	`associate-r`
6×	`pow-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `pow-unpow` `cbrt-unprod`
2×	`unpow-prod-down` `pow-pow` `pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `associate-*l/` `fma-udef` `div-inv`

Counts

4 → 92

Calls

4 calls:

0.0ms	(fma (cos (* 2.0 (* PI u2))) (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 0.5)
9.0ms	(pow (* -2.0 (log u1)) 0.5)
10.0ms	(* PI u2)
37.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.0s

Counts

4 → 12

Calls

4 calls:

591.0ms	(fma (cos (* 2.0 (* PI u2))) (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 0.5)
366.0ms	(pow (* -2.0 (log u1)) 0.5)
22.0ms	(* PI u2)
1.0s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify3.4s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
3	4988
2	1370
1	468
0	194

prune848.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (cos (* 2.0 (* PI u2))) (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* PI u2)
0.3b	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

0.0ms	(fma (cos (* 2.0 (* PI u2))) (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) 0.5)
5.0ms	(pow (* -2.0 (log u1)) 0.5)
5.0ms	(* PI u2)
7.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series1.9s

Counts

4 → 12

Calls

4 calls:

554.0ms	(fma (cos (* 2.0 (* PI u2))) (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) 0.5)
328.0ms	(pow (* -2.0 (log u1)) 0.5)
23.0ms	(* PI u2)
968.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify2.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5004
3	3711
2	1086
1	405
0	186

prune745.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* PI u2)
0.2b	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
0.3b	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
75×	`add-sqr-sqrt`
73×	`*-un-lft-identity` `add-cube-cbrt`
49×	`add-exp-log`
26×	`div-exp`
24×	`associate-/r*`
17×	`unpow-prod-down` `sqr-pow`
13×	`add-cbrt-cube`
10×	`pow1` `pow-exp`
6×	`prod-exp` `div-inv` `associate-/l*`
5×	`pow-to-exp` `rec-exp` `1-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down`
1×	`associate-/r/` `*-commutative` `cbrt-unprod` `pow-flip` `inv-pow` `unswap-sqr`

Counts

4 → 190

Calls

4 calls:

5.0ms	(pow (* -2.0 (log u1)) 0.5)
6.0ms	(* PI u2)
6.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
17.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))

series3.2s

Counts

4 → 12

Calls

4 calls:

364.0ms	(pow (* -2.0 (log u1)) 0.5)
34.0ms	(* PI u2)
1.6s	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
1.1s	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))

simplify1.9s

Counts

202 → 202

Iterations

Iter	Nodes
done	5001
2	2138
1	738
0	302

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI u2)
0.3b	(/ 1 (* 6.0 (pow (/ 1 (* (pow -2.0 1.0) (pow (log u1) 1.0))) 0.5)))
0.3b	(* 6.0 (pow (/ 1 (* (pow -2.0 1.0) (pow (log u1) 1.0))) 0.5))
0.3b	(/ 1 (* (pow -2.0 1.0) (pow (log u1) 1.0)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

428×	`add-exp-log`
268×	`prod-exp`
214×	`pow-exp`
168×	`div-exp`
94×	`pow-to-exp`
84×	`rec-exp` `1-exp`
21×	`add-sqr-sqrt`
18×	`add-cbrt-cube`
14×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
9×	`times-frac`
8×	`pow1` `unpow-prod-down`
6×	`associate-l` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`div-inv` `pow-flip`
2×	`clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `-commutative` `inv-pow` `sqr-pow`

Counts

4 → 260

Calls

4 calls:

11.0ms	(* PI u2)
44.0ms	(/ 1 (* 6.0 (pow (/ 1 (* (pow -2.0 1.0) (pow (log u1) 1.0))) 0.5)))
47.0ms	(* 6.0 (pow (/ 1 (* (pow -2.0 1.0) (pow (log u1) 1.0))) 0.5))
15.0ms	(/ 1 (* (pow -2.0 1.0) (pow (log u1) 1.0)))

series3.3s

Counts

4 → 12

Calls

4 calls:

40.0ms	(* PI u2)
1.0s	(/ 1 (* 6.0 (pow (/ 1 (* (pow -2.0 1.0) (pow (log u1) 1.0))) 0.5)))
1.2s	(* 6.0 (pow (/ 1 (* (pow -2.0 1.0) (pow (log u1) 1.0))) 0.5))
1.0s	(/ 1 (* (pow -2.0 1.0) (pow (log u1) 1.0)))

simplify2.3s

Counts

272 → 272

Iterations

Iter	Nodes
done	5011
2	1615
1	738
0	312

prune889.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes426.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.8s	8000×	body	80	valid
203.0ms	8000×	pre	80	true