Details

sample299.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
5.0ms	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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

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)
0.1b	(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))

rewrite117.0ms

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:

56.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
6.0ms	(pow (* -2.0 (log u1)) 0.5)
17.0ms	(* (* 2.0 PI) u2)
34.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.3s

Counts

4 → 12

Calls

4 calls:

413.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
241.0ms	(pow (* -2.0 (log u1)) 0.5)
30.0ms	(* (* 2.0 PI) u2)
643.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify62.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (53.0ms)

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

prune435.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* (* 2.0 PI) u2)
0.3b	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
0.3b	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

rewrite112.0ms

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×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `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 → 120

Calls

4 calls:

6.0ms	(pow (* -2.0 (log u1)) 0.5)
17.0ms	(* (* 2.0 PI) u2)
58.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
28.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series1.6s

Counts

4 → 12

Calls

4 calls:

245.0ms	(pow (* -2.0 (log u1)) 0.5)
30.0ms	(* (* 2.0 PI) u2)
692.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
652.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify54.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	455	972
1	1801	875
2	5001	871

prune551.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.4b	(* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
0.4b	(/ (fma (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2))) (* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (- (* 0.5 0.5))) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-exp-log`
54×	`prod-exp`
35×	`add-sqr-sqrt`
34×	`add-cbrt-cube`
23×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
21×	`div-exp`
19×	`associate-l`
14×	`pow-exp` `cbrt-unprod`
13×	`associate-r`
9×	`pow1`
8×	`unswap-sqr`
7×	`pow-to-exp`
6×	`cbrt-undiv` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `associate-/r` `-commutative` `div-inv` `associate-/l*`
2×	`unpow-prod-down` `associate-*l/` `associate-/r/`
1×	`flip3--` `frac-2neg` `clear-num` `flip--`

Counts

4 → 144

Calls

4 calls:

18.0ms	(* (* 2.0 PI) u2)
21.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
44.0ms	(* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
105.0ms	(/ (fma (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2))) (* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (- (* 0.5 0.5))) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

series2.2s

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* 2.0 PI) u2)
665.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
655.0ms	(* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
802.0ms	(/ (fma (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2))) (* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (- (* 0.5 0.5))) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

simplify122.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	944	2481
1	4111	2193
2	5003	2164

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fma (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2))) (* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (- (* 0.5 0.5))) (/ 1 (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)))
0.3b	(/ 1 (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.4b	(* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))

rewrite557.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-exp-log`
55×	`prod-exp`
49×	`add-sqr-sqrt`
34×	`times-frac` `add-cbrt-cube`
31×	`*-un-lft-identity`
30×	`add-cube-cbrt`
25×	`associate-r`
24×	`div-exp`
21×	`associate-l`
14×	`pow-exp`
13×	`cbrt-unprod`
11×	`unswap-sqr`
7×	`pow1` `cbrt-undiv` `pow-to-exp`
6×	`sqr-pow`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-/r` `-commutative` `associate-/l*`
2×	`unpow-prod-down` `rec-exp` `flip3--` `1-exp` `associate-*l/` `flip--`
1×	`pow-flip` `frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `un-div-inv` `inv-pow`

Counts

4 → 168

Calls

4 calls:

323.0ms	(* (fma (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2))) (* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (- (* 0.5 0.5))) (/ 1 (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)))
162.0ms	(/ 1 (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
21.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
45.0ms	(* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))

series2.7s

Counts

4 → 12

Calls

4 calls:

805.0ms	(* (fma (* (cos (* (* 2.0 PI) u2)) (cos (* (* 2.0 PI) u2))) (* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (- (* 0.5 0.5))) (/ 1 (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)))
502.0ms	(/ 1 (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
670.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
673.0ms	(* (/ (* 1.0 1.0) (* 6.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))

simplify128.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	980	3170
1	4311	2706
2	5001	2670

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes456.0ms

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	27	14
1	27	14

end0.0ms

sample1.0s

Algorithm

intervals

Results

714.0ms	8000×	body	80	valid
149.0ms	8000×	pre	80	true