Details

sample286.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	18	19
1	35	18
2	71	18
3	153	18
4	403	18
5	1324	18
done	5000	18

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(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)
0.2b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite25.0ms

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)
2.0ms	(pow (* -2.0 (log u1)) 0.5)
6.0ms	(* (* 2.0 PI) u2)
12.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts

4 → 12

Calls

4 calls:

442.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
251.0ms	(pow (* -2.0 (log u1)) 0.5)
31.0ms	(* (* 2.0 PI) u2)
675.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify628.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (159.0ms)

Iter	Nodes	Cost
0	197	1340
1	454	1286
2	1564	1166
done	5001	1166

prune340.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(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)
0.2b	(* (* 2.0 PI) u2)
0.3b	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

rewrite16.0ms

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

series1.4s

Counts

4 → 12

Calls

4 calls:

447.0ms	(fma (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)) 0.5)
258.0ms	(pow (* -2.0 (log u1)) 0.5)
36.0ms	(* (* 2.0 PI) u2)
667.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify534.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (135.0ms)

Iter	Nodes	Cost
0	178	1100
1	403	1053
2	1433	930
done	5000	930

prune288.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cos (* 2.0 (* u2 PI))) (pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5))
0.1b	(pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)
0.2b	(fma 0.16666666666666666 (* (cos (* 2.0 (* u2 PI))) (pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)) 0.5)
0.2b	(* u2 PI)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

160×	`add-exp-log`
148×	`prod-exp`
118×	`pow-exp`
58×	`pow-to-exp`
14×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-prod-down` `unswap-sqr` `sqr-pow`
2×	`unpow-prod-down` `pow-pow` `*-commutative` `cbrt-unprod`
1×	`fma-udef`

Counts

4 → 132

Calls

4 calls:

20.0ms	(* (cos (* 2.0 (* u2 PI))) (pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5))
15.0ms	(pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)
0.0ms	(fma 0.16666666666666666 (* (cos (* 2.0 (* u2 PI))) (pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)) 0.5)
3.0ms	(* u2 PI)

series2.2s

Counts

4 → 12

Calls

4 calls:

543.0ms	(* (cos (* 2.0 (* u2 PI))) (pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5))
1.1s	(pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)
512.0ms	(fma 0.16666666666666666 (* (cos (* 2.0 (* u2 PI))) (pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)) 0.5)
20.0ms	(* u2 PI)

simplify506.0ms

Counts

144 → 144

Iterations

Useful iterations: 2 (147.0ms)

Iter	Nodes	Cost
0	231	3063
1	531	2861
2	1437	2589
done	5000	2589

prune382.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.3b	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
0.5b	(cbrt (pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3))
0.7b	(pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
20×	`cbrt-prod` `add-cbrt-cube`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
14×	`unpow-prod-down` `cube-prod`
13×	`prod-exp`
10×	`pow1` `div-exp` `pow-exp`
5×	`cbrt-unprod` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-r` `pow-prod-down` `associate-/r*` `rem-cube-cbrt`
2×	`cube-div` `cube-mult` `unpow3` `sqr-pow`
1×	`cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `associate-l` `clear-num` `-commutative` `rem-cbrt-cube` `associate-/l`

Counts

4 → 119

Calls

4 calls:

6.0ms	(* (* 2.0 PI) u2)
5.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
3.0ms	(cbrt (pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3))
5.0ms	(pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3)

series2.2s

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) u2)
699.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
675.0ms	(cbrt (pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3))
762.0ms	(pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3)

simplify758.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (319.0ms)

Iter	Nodes	Cost
0	211	2038
1	499	1734
2	1898	1568
done	5001	1568

prune372.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes305.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	18
1	21	18
done	21	18

end0.0ms

sample963.0ms

Algorithm

intervals

Results

683.0ms	8000×	body	80	valid
127.0ms	8000×	pre	80	true