Details

sample312.0ms

Algorithm

intervals

Results

44.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	10
1	71	10
2	154	10
3	469	10
4	1812	10
5	5001	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (* (/ 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))

rewrite54.0ms

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` `add-log-exp`
5×	`cbrt-unprod`
4×	`div-exp` `pow-prod-down` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-*l/` `sum-log` `flip-+` `div-inv`

Counts

4 → 87

Calls

4 calls:

18.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
12.0ms	(pow (* -2.0 (log u1)) 0.5)
7.0ms	(* (* 2.0 PI) u2)
13.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

Counts

4 → 12

Calls

4 calls:

478.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
262.0ms	(pow (* -2.0 (log u1)) 0.5)
36.0ms	(* (* 2.0 PI) u2)
710.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify62.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	507	728
1	2155	656
2	5001	656

prune325.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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`
6×	`add-log-exp`
5×	`div-exp`
4×	`pow-prod-down` `pow-exp` `cbrt-unprod`
3×	`pow-unpow` `times-frac` `associate-r` `associate-/r*`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow`
1×	`+-commutative` `unpow-prod-down` `frac-2neg` `flip3-+` `associate-l` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `associate-/l` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

12.0ms	(+ (* (/ (* 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)
4.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
6.0ms	(* (* 2.0 PI) u2)

series1.5s

Counts

4 → 12

Calls

4 calls:

470.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
272.0ms	(pow (* -2.0 (log u1)) 0.5)
726.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
33.0ms	(* (* 2.0 PI) u2)

simplify55.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	456	597
1	2028	527
2	5002	525

prune270.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log` `add-sqr-sqrt`
33×	`associate-l`
30×	`sqrt-prod`
23×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
19×	`prod-exp`
16×	`add-cbrt-cube`
14×	`pow1`
9×	`associate-r`
7×	`cbrt-unprod`
6×	`pow-exp` `unswap-sqr`
5×	`sqrt-div` `pow-prod-down` `sqr-pow`
4×	`associate-*l/` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow` `div-inv`
1×	`frac-times` `associate-*r/`

Counts

4 → 112

Calls

4 calls:

5.0ms	(pow (* -2.0 (log u1)) 0.5)
6.0ms	(* (* 2.0 PI) u2)
13.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
25.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))

series1.8s

Counts

4 → 12

Calls

4 calls:

269.0ms	(pow (* -2.0 (log u1)) 0.5)
38.0ms	(* (* 2.0 PI) u2)
725.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
758.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))

simplify52.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	447	924
1	1791	827
2	5001	823

prune441.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) (pow (sqrt 0.16666666666666666) 2)) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b	(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
0.3b	(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) (pow (sqrt 0.16666666666666666) 2))
0.3b	(* (* 2.0 PI) u2)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-exp-log`
76×	`pow-exp`
75×	`prod-exp`
40×	`pow-to-exp`
21×	`add-sqr-sqrt`
14×	`associate-r`
12×	`unpow-prod-down`
11×	`add-cbrt-cube`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `unswap-sqr` `sqr-pow`
6×	`associate-l` `add-log-exp`
5×	`sqrt-prod`
4×	`pow-prod-down` `cbrt-unprod`
3×	`pow-unpow` `unpow2`
2×	`pow-pow` `*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 125

Calls

4 calls:

17.0ms	(+ (* (* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) (pow (sqrt 0.16666666666666666) 2)) (cos (* (* 2.0 PI) u2))) 0.5)
4.0ms	(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
12.0ms	(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) (pow (sqrt 0.16666666666666666) 2))
6.0ms	(* (* 2.0 PI) u2)

series2.2s

Counts

4 → 12

Calls

4 calls:

543.0ms	(+ (* (* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) (pow (sqrt 0.16666666666666666) 2)) (cos (* (* 2.0 PI) u2))) 0.5)
921.0ms	(pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5)
747.0ms	(* (pow (* (pow (log u1) 1.0) (pow -2.0 1.0)) 0.5) (pow (sqrt 0.16666666666666666) 2))
39.0ms	(* (* 2.0 PI) u2)

simplify72.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	590	1365
1	2314	1227
2	5002	1220

prune361.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes335.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	13
1	28	13

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
233.0ms	8000×	pre	80	true