Details

sample319.0ms

Algorithm

intervals

Results

47.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify66.0ms

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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

series1.5s

Counts

4 → 12

Calls

4 calls:

464.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
258.0ms	(pow (* -2.0 (log u1)) 0.5)
37.0ms	(* (* 2.0 PI) u2)
702.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify53.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	456	686
1	1839	619
2	5001	619

prune354.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(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	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
0.2b	(* (* 2.0 PI) u2)

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)
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:

461.0ms	(fma (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2)) 0.5)
268.0ms	(pow (* -2.0 (log u1)) 0.5)
695.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
37.0ms	(* (* 2.0 PI) u2)

simplify47.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	405	555
1	1722	486
2	5001	486

prune288.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5)))
0.2b	(* (* 2.0 PI) u2)
0.3b	(/ 1 (/ 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×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `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 → 132

Calls

4 calls:

2.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5)))
7.0ms	(* (* 2.0 PI) u2)
9.0ms	(/ 1 (/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5))))

series1.8s

Counts

4 → 12

Calls

4 calls:

268.0ms	(pow (* -2.0 (log u1)) 0.5)
759.0ms	(/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5)))
31.0ms	(* (* 2.0 PI) u2)
697.0ms	(/ 1 (/ 6.0 (* 1.0 (pow (* -2.0 (log u1)) 0.5))))

simplify61.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	538	1000
1	2316	880
2	5001	844

prune358.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

431×	`add-exp-log`
270×	`prod-exp`
214×	`pow-exp`
168×	`div-exp`
94×	`pow-to-exp`
84×	`rec-exp` `1-exp`
21×	`add-cbrt-cube`
18×	`add-sqr-sqrt`
14×	`associate-r`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`times-frac`
8×	`unpow-prod-down`
6×	`cbrt-unprod` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `div-inv` `unswap-sqr`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `inv-pow` `sqr-pow`

Counts

4 → 260

Calls

4 calls:

6.0ms	(* (* 2.0 PI) u2)
19.0ms	(/ 1 (* 6.0 (pow (/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0))) 0.5)))
8.0ms	(/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0)))
18.0ms	(* 6.0 (pow (/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0))) 0.5))

series2.2s

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) u2)
712.0ms	(/ 1 (* 6.0 (pow (/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0))) 0.5)))
724.0ms	(/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0)))
768.0ms	(* 6.0 (pow (/ 1 (* (pow (log u1) 1.0) (pow -2.0 1.0))) 0.5))

simplify73.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	782	2184
1	2716	2069
2	5001	1951

prune401.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes396.0ms

Accuracy

0% (0.3b 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	27	12
1	27	12

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
241.0ms	8000×	pre	80	true