Details

sample289.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify67.0ms

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

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.4b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* (/ 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))

rewrite40.0ms

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`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `associate-*l/` `fma-udef` `div-inv`

Counts

4 → 92

Calls

4 calls:

1.0ms	(fma (* (/ 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)
5.0ms	(* (* 2.0 PI) u2)
26.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.6s

Counts

4 → 12

Calls

4 calls:

490.0ms	(fma (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)) 0.5)
287.0ms	(pow (* -2.0 (log u1)) 0.5)
35.0ms	(* (* 2.0 PI) u2)
747.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify55.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	456	686
1	1839	619
2	5001	619

prune360.0ms

Filtered

104 candidates to 77 candidates (74.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	93	11	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	11	105

Merged error: 0.0b

Counts

105 → 11

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))

rewrite39.0ms

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:

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)
13.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series1.9s

Counts

4 → 12

Calls

4 calls:

280.0ms	(pow (* -2.0 (log u1)) 0.5)
790.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
40.0ms	(* (* 2.0 PI) u2)
748.0ms	(* (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

prune460.0ms

Filtered

132 candidates to 97 candidates (73.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	132	11	143

Merged error: 0.0b

Counts

143 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

141×	`pow1`
77×	`pow-prod-down`
60×	`sqrt-pow1`
36×	`add-exp-log`
28×	`add-sqr-sqrt`
21×	`add-cbrt-cube`
19×	`associate-l`
18×	`add-cube-cbrt` `*-un-lft-identity`
17×	`prod-exp` `pow-prod-up`
15×	`associate-r`
12×	`pow1/2`
11×	`times-frac` `pow-sqr`
9×	`cbrt-unprod`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `swap-sqr` `div-exp` `pow-exp` `sqrt-prod` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`sqr-pow`
2×	`pow-to-exp`
1×	`cbrt-undiv` `pow2` `unpow-prod-down` `pow-plus` `sqrt-unprod` `associate-*l/` `rem-square-sqrt` `div-inv`

Counts

4 → 151

Calls

4 calls:

5.0ms	(* (* 2.0 PI) u2)
5.0ms	(* (* 2.0 PI) u2)
8.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
12.0ms	(* (sqrt (* (* 2.0 PI) u2)) (sqrt (* (* 2.0 PI) u2)))

series911.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* 2.0 PI) u2)
34.0ms	(* (* 2.0 PI) u2)
729.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
108.0ms	(* (sqrt (* (* 2.0 PI) u2)) (sqrt (* (* 2.0 PI) u2)))

simplify73.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	495	718
1	2244	631
2	5003	610

prune388.0ms

Filtered

163 candidates to 83 candidates (50.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	163	11	174

Merged error: 0.0b

Counts

174 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
23×	`prod-exp`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `add-cbrt-cube`
11×	`pow1` `times-frac`
9×	`rem-log-exp`
8×	`div-exp` `associate-r` `pow-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `pow-to-exp` `exp-prod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-*l/` `sqr-pow`
2×	`log-div` `log-prod` `log-pow` `*-commutative`
1×	`cbrt-undiv` `unpow-prod-down` `exp-diff` `exp-sum` `div-inv` `rem-exp-log`

Counts

4 → 100

Calls

4 calls:

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

series2.4s

Counts

4 → 12

Calls

4 calls:

887.0ms	(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
34.0ms	(* (* 2.0 PI) u2)
735.0ms	(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
731.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify46.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	404	675
1	1608	609
2	5002	608

prune354.0ms

Filtered

112 candidates to 79 candidates (70.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	112	11	123

Merged error: 0.0b

Counts

123 → 11

regimes506.0ms

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	24	13
1	24	13

end0.0ms

sample1.2s

Algorithm

intervals

Results

795.0ms	8000×	body	80	valid
201.0ms	8000×	pre	80	true