Details

sample202.0ms

Algorithm

intervals

Results

58.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1122
3	229
2	78
1	37
0	18

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/6 (cos (* (* PI u2) 2)))
0.2b	(pow (* -2 (log u1)) 0.5)
0.3b	(* PI u2)
0.4b	(fma (* 1/6 (cos (* (* PI u2) 2))) (pow (* -2 (log u1)) 0.5) 0.5)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`pow1` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-prod-down` `prod-exp`
2×	`pow-pow` `pow-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow-to-exp` `unpow-prod-down` `fma-udef` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

32.0ms	(* 1/6 (cos (* (* PI u2) 2)))
5.0ms	(pow (* -2 (log u1)) 0.5)
6.0ms	(* PI u2)
1.0ms	(fma (* 1/6 (cos (* (* PI u2) 2))) (pow (* -2 (log u1)) 0.5) 0.5)

series846.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* 1/6 (cos (* (* PI u2) 2)))
374.0ms	(pow (* -2 (log u1)) 0.5)
39.0ms	(* PI u2)
356.0ms	(fma (* 1/6 (cos (* (* PI u2) 2))) (pow (* -2 (log u1)) 0.5) 0.5)

simplify1.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
2	1277
1	382
0	164

prune505.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
0.2b	(pow (* -2 (log u1)) 0.5)
0.3b	(* (* 2 PI) u2)
0.4b	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
25×	`add-sqr-sqrt`
24×	`prod-exp`
16×	`*-un-lft-identity`
14×	`add-cbrt-cube` `associate-l` `add-cube-cbrt`
13×	`times-frac`
12×	`pow1`
10×	`pow-exp`
8×	`div-exp` `associate-r`
6×	`add-log-exp` `unswap-sqr`
5×	`pow-to-exp` `cbrt-unprod` `sqr-pow`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `pow-prod-down` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `sum-log` `fma-def` `flip3-+` `associate-*l/` `flip-+` `div-inv`

Counts

4 → 110

Calls

4 calls:

110.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
10.0ms	(pow (* -2 (log u1)) 0.5)
30.0ms	(* (* 2 PI) u2)
35.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

series2.1s

Counts

4 → 12

Calls

4 calls:

661.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
348.0ms	(pow (* -2 (log u1)) 0.5)
53.0ms	(* (* 2 PI) u2)
1.1s	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

simplify1.9s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	2728
1	607
0	226

prune759.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ (pow (* -2 (log u1)) 0.5) 6) (cos (* (* 2 PI) u2))) 0.5)
0.2b	(pow (* -2 (log u1)) 0.5)
0.3b	(/ (pow (* -2 (log u1)) 0.5) 6)
0.3b	(* (* 2 PI) u2)

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
16×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
15×	`times-frac`
12×	`pow1`
11×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`unpow-prod-down` `prod-exp` `associate-/l*` `sqr-pow`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `pow-exp` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `associate-/r` `associate-r*` `cbrt-unprod`
2×	`pow-to-exp` `pow-pow`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `flip3-+` `associate-l` `*-commutative` `flip-+` `div-inv`

Counts

4 → 97

Calls

4 calls:

60.0ms	(+ (* (/ (pow (* -2 (log u1)) 0.5) 6) (cos (* (* 2 PI) u2))) 0.5)
5.0ms	(pow (* -2 (log u1)) 0.5)
8.0ms	(/ (pow (* -2 (log u1)) 0.5) 6)
15.0ms	(* (* 2 PI) u2)

series2.3s

Counts

4 → 12

Calls

4 calls:

685.0ms	(+ (* (/ (pow (* -2 (log u1)) 0.5) 6) (cos (* (* 2 PI) u2))) 0.5)
441.0ms	(pow (* -2 (log u1)) 0.5)
1.1s	(/ (pow (* -2 (log u1)) 0.5) 6)
41.0ms	(* (* 2 PI) u2)

simplify1.7s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	2159
1	510
0	208

prune990.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
0.2b	(pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)
0.3b	(* (* 2 PI) u2)
0.4b	(* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
33×	`prod-exp`
32×	`pow-exp`
14×	`pow-to-exp`
11×	`add-sqr-sqrt` `add-cbrt-cube`
10×	`pow1`
8×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `sqr-pow`
2×	`unpow-prod-down` `pow-pow` `*-commutative` `unswap-sqr`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 98

Calls

4 calls:

55.0ms	(+ (* (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
8.0ms	(pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)
31.0ms	(* (* 2 PI) u2)
34.0ms	(* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))

series3.0s

Counts

4 → 12

Calls

4 calls:

588.0ms	(+ (* (* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
1.3s	(pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5)
50.0ms	(* (* 2 PI) u2)
986.0ms	(* 1/6 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 0.5))

simplify3.5s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	2283
1	586
0	218

prune664.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes648.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.1s	8000×	body	80	valid
446.0ms	8000×	pre	80	true