Details

sample286.0ms

Algorithm

intervals

Results

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

simplify65.0ms

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

localize19.0ms

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)
0.4b	(* (/ 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:

26.0ms	(+ (* (* (/ 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:

451.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
270.0ms	(pow (* -2.0 (log u1)) 0.5)
31.0ms	(* (* 2.0 PI) u2)
686.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify60.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

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

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: 0.0b

Counts

100 → 8

localize20.0ms

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

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	(* (* 2.0 PI) u2)
5.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

448.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
261.0ms	(pow (* -2.0 (log u1)) 0.5)
36.0ms	(* (* 2.0 PI) u2)
680.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (11.0ms)

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

prune286.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	95	9	104

Merged error: 0b

Counts

104 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

330×	`add-exp-log`
219×	`prod-exp`
118×	`pow1`
90×	`add-cbrt-cube`
66×	`pow-prod-down`
65×	`div-exp`
56×	`cbrt-unprod`
42×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`pow-exp`
16×	`pow-to-exp`
14×	`associate-/l*`
11×	`cbrt-undiv`
9×	`associate-/r*` `pow-sqr` `pow-prod-up`
8×	`unpow-prod-down` `sqr-pow`
5×	`associate-r/` `associate-l/`
4×	`add-log-exp` `difference-of-squares`
3×	`frac-2neg` `pow-plus` `clear-num` `div-inv`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `div-sub` `swap-sqr` `associate-r` `associate-l` `*-commutative`

Counts

4 → 222

Calls

4 calls:

5.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
5.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
29.0ms	(/ (- (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))
21.0ms	(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))

series2.6s

Counts

4 → 12

Calls

4 calls:

678.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
710.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
746.0ms	(/ (- (* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5))
458.0ms	(* (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))))

simplify132.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	938	4142
1	4166	3212
2	5003	3145

prune549.0ms

Filtered

234 candidates to 117 candidates (50.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	234	9	243

Merged error: 0b

Counts

243 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.6b	(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)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log`
27×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
15×	`add-cbrt-cube`
14×	`associate-l`
13×	`prod-exp`
12×	`cbrt-prod`
11×	`times-frac`
10×	`pow1`
8×	`associate-r`
7×	`unpow-prod-down`
6×	`cube-prod`
5×	`pow-exp` `cbrt-unprod` `sqr-pow`
4×	`cube-div` `div-exp` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `pow-unpow` `pow-prod-down`
2×	`cube-mult` `cbrt-div` `flip3-+` `unpow3` `*-commutative` `flip-+`
1×	`cbrt-undiv` `pow-pow` `pow1/3` `associate-*l/` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 107

Calls

4 calls:

5.0ms	(* (* 2.0 PI) u2)
12.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
9.0ms	(cbrt (pow (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5) 3))
10.0ms	(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:

31.0ms	(* (* 2.0 PI) u2)
694.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
460.0ms	(cbrt (pow (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5) 3))
602.0ms	(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

119 → 119

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	677	1433
1	2923	1315
2	5001	1306

prune324.0ms

Filtered

119 candidates to 77 candidates (64.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	119	9	128

Merged error: 0b

Counts

128 → 9

regimes564.0ms

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

sample928.0ms

Algorithm

intervals

Results

649.0ms	8000×	body	80	valid
131.0ms	8000×	pre	80	true

Details

sample286.0ms

simplify65.0ms

prune5.0ms

localize19.0ms

rewrite48.0ms

series1.4s

simplify60.0ms

prune299.0ms

localize20.0ms

rewrite24.0ms

series1.4s

simplify54.0ms

prune286.0ms

localize28.0ms

rewrite77.0ms

series2.6s

simplify132.0ms

prune549.0ms

localize20.0ms

rewrite38.0ms

series1.8s

simplify88.0ms

prune324.0ms

regimes564.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample928.0ms

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