Details

sample292.0ms

Algorithm

intervals

Results

23.0ms	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	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:

0.0b	(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)
4.0ms	(pow (* -2.0 (log u1)) 0.5)
20.0ms	(* (* 2.0 PI) u2)
11.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.4s

Counts

4 → 12

Calls

4 calls:

454.0ms	(fma (* (/ 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)
31.0ms	(* (* 2.0 PI) u2)
690.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify52.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (11.0ms)

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

prune330.0ms

Filtered

104 candidates to 77 candidates (74.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	8	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 0b

Counts

105 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* 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)
0.3b	(* (* 2.0 PI) u2)
0.3b	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

rewrite17.0ms

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

Counts

4 → 89

Calls

4 calls:

1.0ms	(fma (* 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:

457.0ms	(fma (* 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)
31.0ms	(* (* 2.0 PI) u2)
684.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	387	666
1	1508	612
2	5001	612

prune298.0ms

Filtered

101 candidates to 78 candidates (77.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	101	8	109

Merged error: 0b

Counts

109 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(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))

rewrite27.0ms

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))

series2.2s

Counts

4 → 12

Calls

4 calls:

801.0ms	(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
31.0ms	(* (* 2.0 PI) u2)
682.0ms	(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
676.0ms	(* (/ 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

prune369.0ms

Filtered

112 candidates to 78 candidates (69.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	112	8	120

Merged error: 0b

Counts

120 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (* (/ 1.0 6.0) (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))
0.4b	(expm1 (log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

1.0ms	(log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
5.0ms	(* (* 2.0 PI) u2)
8.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.0ms	(expm1 (log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))

series2.5s

Counts

4 → 12

Calls

4 calls:

840.0ms	(log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
31.0ms	(* (* 2.0 PI) u2)
716.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
887.0ms	(expm1 (log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))

simplify47.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	394	641
1	1461	570
2	5001	570

prune298.0ms

Filtered

97 candidates to 69 candidates (71.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	97	8	105

Merged error: 0b

Counts

105 → 8

regimes395.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample1.1s

Algorithm

intervals

Results

784.0ms	8000×	body	80	valid
130.0ms	8000×	pre	80	true