Details

sample287.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify69.0ms

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

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.4b

Counts

2 → 1

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
37×	`associate-l`
32×	`add-exp-log`
31×	`-un-lft-identity` `associate-r*`
30×	`unpow-prod-down`
25×	`add-cube-cbrt`
16×	`pow1` `unswap-sqr`
14×	`prod-exp` `add-cbrt-cube`
13×	`times-frac`
9×	`associate-*l/`
6×	`pow-exp` `add-log-exp`
5×	`pow-prod-down` `*-commutative` `cbrt-unprod`
4×	`div-exp` `sqr-pow`
3×	`pow-to-exp` `pow-unpow` `associate-/r` `distribute-lft-out` `associate-/l`
2×	`pow-pow` `log-pow`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `div-inv`

Counts

4 → 140

Calls

4 calls:

40.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
5.0ms	(pow (* -2.0 (log u1)) 0.5)
8.0ms	(* (* 2.0 PI) u2)
34.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

Counts

4 → 12

Calls

4 calls:

474.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
273.0ms	(pow (* -2.0 (log u1)) 0.5)
34.0ms	(* (* 2.0 PI) u2)
720.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify82.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	675	1047
1	3042	976
2	5001	976

prune384.0ms

Filtered

152 candidates to 109 candidates (28.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	146	6	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	6	153

Merged error: 0b

Counts

153 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
0.3b	(* (* 2.0 PI) u2)

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

383×	`times-frac`
233×	`add-sqr-sqrt`
200×	`*-un-lft-identity`
196×	`add-cube-cbrt`
195×	`unpow-prod-down`
66×	`associate-r`
61×	`associate-l`
32×	`add-exp-log`
27×	`pow1`
20×	`associate-/l*`
19×	`div-inv` `unswap-sqr`
17×	`*-commutative`
16×	`associate-/r*`
15×	`log-pow` `sqr-pow`
14×	`add-cbrt-cube`
12×	`div-exp`
9×	`associate-/r/`
6×	`pow-exp` `prod-exp` `add-log-exp`
4×	`pow-prod-down`
3×	`cbrt-undiv` `pow-to-exp` `pow-unpow` `cbrt-unprod`
2×	`pow-pow` `frac-2neg` `clear-num` `distribute-lft-out`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 353

Calls

4 calls:

105.0ms	(+ (* (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) (cos (* (* 2.0 PI) u2))) 0.5)
5.0ms	(pow (* -2.0 (log u1)) 0.5)
19.0ms	(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
7.0ms	(* (* 2.0 PI) u2)

series1.5s

Counts

4 → 12

Calls

4 calls:

466.0ms	(+ (* (/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0)) (cos (* (* 2.0 PI) u2))) 0.5)
269.0ms	(pow (* -2.0 (log u1)) 0.5)
710.0ms	(/ (pow (* -2.0 (log u1)) 0.5) (/ 6.0 1.0))
33.0ms	(* (* 2.0 PI) u2)

simplify76.0ms

Algorithm

egg-herbie

Counts

365 → 365

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1334	3818
1	5002	3733

prune907.0ms

Filtered

365 candidates to 259 candidates (29.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	364	1	365
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	365	6	371

Merged error: 0b

Counts

371 → 6

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite575.0ms

Algorithm

rewrite-expression-head

Rules

980×	`add-sqr-sqrt`
707×	`*-un-lft-identity`
554×	`associate-l`
404×	`unswap-sqr`
401×	`times-frac`
221×	`distribute-lft-out`
170×	`difference-of-squares`
153×	`distribute-rgt-neg-in`
128×	`add-cube-cbrt`
119×	`associate-*l/`
116×	`unpow-prod-down`
103×	`add-exp-log`
81×	`frac-times`
80×	`associate-/l*`
79×	`associate-/r*`
61×	`associate-r`
55×	`swap-sqr`
54×	`prod-exp`
51×	`distribute-lft-out--`
47×	`sqr-pow`
34×	`add-cbrt-cube`
23×	`clear-num`
22×	`frac-2neg`
21×	`div-exp`
18×	`pow1`
14×	`pow-exp` `cbrt-unprod`
12×	`*-commutative`
9×	`associate-*r/`
8×	`pow-prod-down`
7×	`pow-to-exp`
6×	`cbrt-undiv` `div-inv`
4×	`add-log-exp`
2×	`associate-/r/` `log-pow` `un-div-inv` `associate-/l/`
1×	`pow2` `neg-sub0` `associate-+l-` `pow-unpow` `flip3--` `flip3-+` `div-sub` `flip--` `flip-+`

Counts

4 → 640

Calls

4 calls:

7.0ms	(* (* 2.0 PI) u2)
52.0ms	(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
16.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
436.0ms	(/ (+ (- (* 0.5 0.5)) (* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (* (cos (* 2.0 (* u2 PI))) (cos (* 2.0 (* u2 PI)))))) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

series2.3s

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* 2.0 PI) u2)
735.0ms	(* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5)))
722.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
785.0ms	(/ (+ (- (* 0.5 0.5)) (* (* (* (/ 1.0 6.0) (/ 1.0 6.0)) (pow (* -2.0 (log u1)) (* 2 0.5))) (* (cos (* 2.0 (* u2 PI))) (cos (* 2.0 (* u2 PI)))))) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))

simplify190.0ms

Algorithm

egg-herbie

Counts

652 → 652

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2057	17310
1	5001	16841

prune1.9s

Filtered

652 candidates to 288 candidates (55.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	652	0	652
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	652	6	658

Merged error: 0b

Counts

658 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.5b	(cbrt (pow (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5) 3))
0.7b	(pow (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5) 3)

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
37×	`associate-l`
30×	`add-exp-log`
29×	`unpow-prod-down`
27×	`associate-r`
25×	`add-cube-cbrt`
15×	`add-cbrt-cube` `unswap-sqr`
13×	`pow1` `times-frac` `prod-exp`
11×	`cbrt-prod`
9×	`associate-*l/`
6×	`distribute-lft-out`
5×	`pow-exp` `cbrt-unprod` `sqr-pow`
4×	`pow-unpow` `div-exp` `pow-prod-down` `*-commutative` `add-log-exp`
3×	`pow-to-exp` `associate-/r` `associate-/l`
2×	`unpow3` `rem-cbrt-cube`
1×	`cbrt-undiv` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `log-pow` `div-inv` `rem-cube-cbrt`

Counts

4 → 140

Calls

4 calls:

8.0ms	(* (* 2.0 PI) u2)
18.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
35.0ms	(cbrt (pow (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5) 3))
39.0ms	(pow (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5) 3)

series1.8s

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* 2.0 PI) u2)
703.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
467.0ms	(cbrt (pow (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5) 3))
625.0ms	(pow (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5) 3)

simplify88.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	755	1376
1	3405	1276
2	5001	1270

prune415.0ms

Filtered

152 candidates to 103 candidates (32.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	152	6	158

Merged error: 0b

Counts

158 → 6

regimes369.0ms

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	23	10
1	23	10

end0.0ms

sample915.0ms

Algorithm

intervals

Results

644.0ms	8000×	body	80	valid
128.0ms	8000×	pre	80	true