Details

sample289.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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:

0.1b	(+ (* (* (/ 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))

rewrite48.0ms

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:

9.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
19.0ms	(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:

451.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
265.0ms	(pow (* -2.0 (log u1)) 0.5)
31.0ms	(* (* 2.0 PI) u2)
687.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify61.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

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

prune338.0ms

Filtered

99 candidates to 71 candidates (71.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	86	13	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	13	100

Merged error: 0.0b

Counts

100 → 13

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

rewrite35.0ms

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)
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)
9.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series1.7s

Counts

4 → 12

Calls

4 calls:

263.0ms	(pow (* -2.0 (log u1)) 0.5)
726.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
31.0ms	(* (* 2.0 PI) u2)
691.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify54.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	447	924
1	1791	827
2	5002	823

prune426.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	119	5	124
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	129	8	137

Merged error: 0.0b

Counts

137 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI))))) 0.5)
0.1b	(pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)
0.3b	(* u2 PI)
0.3b	(* 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

195×	`add-exp-log`
182×	`prod-exp`
118×	`pow-exp`
58×	`pow-to-exp`
11×	`add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`pow1`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l` `add-log-exp`
4×	`associate-r` `pow-prod-down` `cbrt-unprod`
3×	`pow-unpow`
2×	`pow-pow` `*-commutative`
1×	`+-commutative` `unpow-prod-down` `flip3-+` `sum-log` `flip-+` `unswap-sqr` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

9.0ms	(+ (* 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI))))) 0.5)
11.0ms	(pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)
4.0ms	(* u2 PI)
13.0ms	(* 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

590.0ms	(+ (* 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI))))) 0.5)
1.1s	(pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)
26.0ms	(* u2 PI)
602.0ms	(* 0.16666666666666666 (* (pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5) (cos (* 2.0 (* u2 PI)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	589	1613
1	1758	1497
2	5002	1497

prune299.0ms

Filtered

136 candidates to 52 candidates (38.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	136	8	144

Merged error: 0.0b

Counts

144 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.3b	(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
0.6b	(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt 6.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log`
24×	`prod-exp`
23×	`add-cbrt-cube`
19×	`sqrt-prod`
18×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
17×	`associate-l`
15×	`times-frac`
14×	`pow1`
9×	`cbrt-unprod`
6×	`div-exp` `pow-exp` `associate-/r*`
5×	`pow-prod-down`
4×	`associate-r` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-unpow`
2×	`pow-pow` `sqrt-div` `associate-l/` `-commutative` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `associate-/l/` `associate-/l*` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

4.0ms	(pow (* -2.0 (log u1)) 0.5)
5.0ms	(* (* 2.0 PI) u2)
11.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
12.0ms	(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt 6.0))

series1.9s

Counts

4 → 12

Calls

4 calls:

263.0ms	(pow (* -2.0 (log u1)) 0.5)
39.0ms	(* (* 2.0 PI) u2)
757.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)))
812.0ms	(/ (* (sqrt (/ 1.0 6.0)) (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt 6.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	520	963
1	2146	864
2	5001	860

prune376.0ms

Filtered

114 candidates to 74 candidates (64.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	114	8	122

Merged error: 0.0b

Counts

122 → 8

regimes550.0ms

Accuracy

0% (0.4b 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	33	14
1	33	14

end0.0ms

sample1.2s

Algorithm

intervals

Results

760.0ms	8000×	body	80	valid
332.0ms	8000×	pre	80	true