Details

sample288.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	9
1	74	9
2	160	9
3	483	9
4	1845	9
5	5001	9

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

rewrite55.0ms

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×	`expm1-log1p-u` `div-exp` `pow-prod-down` `log1p-expm1-u` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `fma-def` `flip3-+` `associate-*l/` `sum-log` `flip-+` `div-inv`

Counts

4 → 96

Calls

4 calls:

28.0ms	(+ (* (* (/ 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)
7.0ms	(* (* 2.0 PI) u2)
14.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

Counts

4 → 12

Calls

4 calls:

467.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
268.0ms	(pow (* -2.0 (log u1)) 0.5)
33.0ms	(* (* 2.0 PI) u2)
691.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify65.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	523	772
1	2229	700
2	5001	697

prune358.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize17.0ms

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

rewrite28.0ms

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×	`expm1-log1p-u` `pow-prod-down` `pow-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`pow-unpow` `times-frac` `associate-r` `associate-/r*`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow`
1×	`+-commutative` `unpow-prod-down` `fma-def` `frac-2neg` `flip3-+` `associate-l` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `associate-/l` `sqr-pow`

Counts

4 → 79

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

series1.5s

Counts

4 → 12

Calls

4 calls:

469.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
271.0ms	(pow (* -2.0 (log u1)) 0.5)
709.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
37.0ms	(* (* 2.0 PI) u2)

simplify56.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	472	641
1	2101	569
2	5002	564

prune288.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
72×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log`
24×	`associate-/r*`
17×	`unpow-prod-down` `sqr-pow`
16×	`add-cbrt-cube`
13×	`div-exp`
12×	`pow1`
6×	`pow-exp` `prod-exp` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-r` `cbrt-unprod`
2×	`pow-pow` `frac-2neg` `clear-num`
1×	`associate-l` `associate-/r/` `*-commutative`

Counts

4 → 178

Calls

4 calls:

2.0ms	(pow (* -2.0 (log u1)) 0.5)
7.0ms	(/ 1.0 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
6.0ms	(* (* 2.0 PI) u2)
3.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))

series1.8s

Counts

4 → 12

Calls

4 calls:

266.0ms	(pow (* -2.0 (log u1)) 0.5)
707.0ms	(/ 1.0 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
32.0ms	(* (* 2.0 PI) u2)
774.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))

simplify80.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	695	1598
1	3034	1524
2	5002	1524

prune641.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

936×	`add-exp-log`
708×	`prod-exp`
440×	`pow-exp`
283×	`div-exp`
254×	`pow-to-exp`
93×	`rec-exp` `1-exp`
25×	`add-cbrt-cube`
18×	`add-sqr-sqrt`
14×	`associate-r`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`times-frac`
8×	`unpow-prod-down` `cbrt-unprod`
6×	`associate-/l*`
5×	`cbrt-undiv` `pow-prod-down`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`pow-flip` `frac-2neg` `clear-num` `associate-/r` `-commutative` `sqr-pow`
1×	`inv-pow`

Counts

4 → 380

Calls

4 calls:

32.0ms	(* 6.0 (pow (/ 1 (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0)))) 0.5))
27.0ms	(/ 1 (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))))
24.0ms	(/ 1.0 (* 6.0 (pow (/ 1 (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0)))) 0.5)))
7.0ms	(* (* 2.0 PI) u2)

series3.1s

Counts

4 → 12

Calls

4 calls:

1.1s	(* 6.0 (pow (/ 1 (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0)))) 0.5))
1.0s	(/ 1 (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))))
964.0ms	(/ 1.0 (* 6.0 (pow (/ 1 (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0)))) 0.5)))
32.0ms	(* (* 2.0 PI) u2)

simplify104.0ms

Algorithm

egg-herbie

Counts

392 → 392

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	1016	4165
1	3291	3996
2	5002	3987

prune461.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes410.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample921.0ms

Algorithm

intervals

Results

637.0ms	8000×	body	80	valid
129.0ms	8000×	pre	80	true