Details

sample297.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify64.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* (/ 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)
0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite53.0ms

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:

27.0ms	(+ (* (* (/ 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)
13.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts

4 → 12

Calls

4 calls:

452.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
264.0ms	(pow (* -2.0 (log u1)) 0.5)
31.0ms	(* (* 2.0 PI) u2)
686.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify61.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

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

prune329.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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:

11.0ms	(+ (* (/ (* 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)
7.0ms	(* (* 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:

454.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
265.0ms	(pow (* -2.0 (log u1)) 0.5)
38.0ms	(* (* 2.0 PI) u2)
690.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	456	597
1	2028	527
2	5001	525

prune266.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.3b	(/ 1 (/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5))))
0.3b	(/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
36×	`times-frac`
32×	`div-exp`
24×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `prod-exp`
23×	`add-cbrt-cube`
13×	`pow1`
10×	`pow-exp`
8×	`associate-/r*`
7×	`cbrt-undiv`
6×	`rec-exp` `1-exp` `div-inv` `associate-/l*`
5×	`pow-to-exp` `cbrt-unprod`
4×	`pow-prod-down` `add-log-exp`
3×	`pow-unpow` `associate-r`
2×	`pow-pow` `frac-2neg` `clear-num`
1×	`unpow-prod-down` `pow-flip` `associate-l` `associate-/r/` `*-commutative` `inv-pow` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

3.0ms	(pow (* -2.0 (log u1)) 0.5)
6.0ms	(* (* 2.0 PI) u2)
8.0ms	(/ 1 (/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5))))
4.0ms	(/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5)))

series1.7s

Counts

4 → 12

Calls

4 calls:

268.0ms	(pow (* -2.0 (log u1)) 0.5)
31.0ms	(* (* 2.0 PI) u2)
696.0ms	(/ 1 (/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5))))
750.0ms	(/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5)))

simplify59.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	530	960
1	2306	840
2	5001	804

prune316.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

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

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

342×	`add-exp-log`
213×	`prod-exp`
96×	`add-cbrt-cube`
81×	`div-exp`
50×	`cbrt-unprod`
43×	`pow1`
32×	`pow-exp`
21×	`cbrt-undiv`
18×	`times-frac`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-prod-down`
16×	`pow-to-exp`
9×	`associate-/r*`
6×	`associate-/l*`
5×	`associate-*l/`
4×	`pow-sqr` `pow-prod-up` `add-log-exp` `difference-of-squares`
3×	`frac-2neg` `clear-num` `div-inv`
2×	`flip3--` `pow-plus` `associate-/r/` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `div-sub` `associate-r/` `swap-sqr` `associate-r` `associate-l` `-commutative`

Counts

4 → 178

Calls

4 calls:

4.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
4.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
195.0ms	(/ (- (* (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5))
72.0ms	(* (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))))

series2.6s

Counts

4 → 12

Calls

4 calls:

711.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
692.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
772.0ms	(/ (- (* (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5))
457.0ms	(* (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))))

simplify112.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	897	3821
1	4139	2864
2	5002	2794

prune461.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes279.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	11
1	28	11

end0.0ms

sample990.0ms

Algorithm

intervals

Results

695.0ms	8000×	body	80	valid
137.0ms	8000×	pre	80	true