Details

sample284.0ms

Algorithm

intervals

Results

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

simplify67.0ms

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 (0.0%)

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

rewrite47.0ms

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:

24.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
4.0ms	(pow (* -2.0 (log u1)) 0.5)
5.0ms	(* (* 2.0 PI) u2)
10.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts

4 → 12

Calls

4 calls:

453.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
263.0ms	(pow (* -2.0 (log u1)) 0.5)
32.0ms	(* (* 2.0 PI) u2)
699.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify61.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (13.0ms)

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

prune299.0ms

Filtered

99 candidates to 71 candidates (71.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	8	100

Merged error: 0b

Counts

100 → 8

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
12×	`pow1`
11×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`unpow-prod-down` `prod-exp` `associate-/l*` `sqr-pow`
4×	`div-exp` `pow-prod-down` `pow-exp`
3×	`pow-unpow` `associate-r` `associate-/r*` `cbrt-unprod`
2×	`pow-to-exp` `pow-pow`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `associate-l` `clear-num` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 84

Calls

4 calls:

8.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
4.0ms	(pow (* -2.0 (log u1)) 0.5)
5.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
5.0ms	(* (* 2.0 PI) u2)

series1.4s

Counts

4 → 12

Calls

4 calls:

459.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
262.0ms	(pow (* -2.0 (log u1)) 0.5)
689.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
32.0ms	(* (* 2.0 PI) u2)

simplify55.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	438	710
1	1838	655
2	5001	655

prune284.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	96	8	104

Merged error: 0b

Counts

104 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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×	`associate-*l/` `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 → 112

Calls

4 calls:

4.0ms	(pow (* -2.0 (log u1)) 0.5)
9.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
12.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
5.0ms	(* (* 2.0 PI) u2)

series1.8s

Counts

4 → 12

Calls

4 calls:

259.0ms	(pow (* -2.0 (log u1)) 0.5)
760.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
725.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
37.0ms	(* (* 2.0 PI) u2)

simplify58.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	447	924
1	1791	827
2	5001	823

prune379.0ms

Filtered

124 candidates to 90 candidates (72.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	124	8	132

Merged error: 0b

Counts

132 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) u2)
0.3b	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
0.6b	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
0.7b	(pow (pow (* -2.0 (log u1)) 0.5) 3)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
44×	`cbrt-prod`
25×	`unpow-prod-down`
22×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
19×	`cube-prod`
18×	`add-exp-log`
16×	`times-frac`
15×	`sqr-pow`
14×	`associate-l` `unswap-sqr`
13×	`add-cbrt-cube`
11×	`pow1`
6×	`pow-exp` `prod-exp`
5×	`cbrt-unprod`
4×	`pow-prod-down` `add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow3`
2×	`pow-to-exp` `*-commutative`
1×	`cbrt-undiv` `pow-pow` `pow1/3` `div-exp` `associate-*l/` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 133

Calls

4 calls:

5.0ms	(* (* 2.0 PI) u2)
13.0ms	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
3.0ms	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
4.0ms	(pow (pow (* -2.0 (log u1)) 0.5) 3)

series1.7s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (* 2.0 PI) u2)
711.0ms	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
668.0ms	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
314.0ms	(pow (pow (* -2.0 (log u1)) 0.5) 3)

simplify73.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	614	1021
1	2541	978
2	5001	962

prune353.0ms

Filtered

145 candidates to 87 candidates (60.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	145	8	153

Merged error: 0b

Counts

153 → 8

regimes527.0ms

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	24	10
1	24	10

end0.0ms

sample947.0ms

Algorithm

intervals

Results

673.0ms	8000×	body	80	valid
126.0ms	8000×	pre	80	true