Details

sample158.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

7.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	7	4

prune3.0ms

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: 29.8b

Counts

2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

27.9b

(sqrt (+ (* re re) (* im im)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
1×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

3.0ms

(sqrt (+ (* re re) (* im im)))

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

(sqrt (+ (* re re) (* im im)))

simplify135.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 5 (132.0ms)

Iter	Nodes	Cost
0	89	100
1	215	97
2	503	97
3	1265	97
4	4227	97
5	5002	96

prune33.0ms

Filtered

15 candidates to 18 candidates (-20.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	14	4	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	5	19

Merged error: 7.1b

Counts

19 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (+ (* re re) (* im im))))
0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
28.9b	(cbrt (+ (* re re) (* im im)))
28.9b	(cbrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`cbrt-prod` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`cbrt-div`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `associate-*r/`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 74

Calls

4 calls:

4.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
7.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
3.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))

series98.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
37.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
21.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))

simplify107.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	311	925
1	1082	871
2	4121	841
3	5001	813

prune110.0ms

Filtered

72 candidates to 86 candidates (-19.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	86	5	91

Merged error: 7.1b

Counts

91 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (+ (* re re) (* im im))))
0.3b	(* (fabs (pow (+ (* re re) (* im im)) 1/3)) (sqrt (cbrt (+ (* re re) (* im im)))))
28.9b	(cbrt (+ (* re re) (* im im)))
31.2b	(pow (+ (* re re) (* im im)) 1/3)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
14×	`sqrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cbrt-prod`
9×	`associate-r`
8×	`pow1`
7×	`add-exp-log`
6×	`cbrt-div` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `flip3-+` `associate-l` `flip-+` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/3` `associate-*r/`
1×	`pow-to-exp` `pow-pow` `pow1/2` `unpow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

4.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
7.0ms	(* (fabs (pow (+ (* re re) (* im im)) 1/3)) (sqrt (cbrt (+ (* re re) (* im im)))))
3.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(pow (+ (* re re) (* im im)) 1/3)

series97.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
33.0ms	(* (fabs (pow (+ (* re re) (* im im)) 1/3)) (sqrt (cbrt (+ (* re re) (* im im)))))
22.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(pow (+ (* re re) (* im im)) 1/3)

simplify44.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	359	914
1	1339	842
2	5001	801

prune144.0ms

Filtered

70 candidates to 91 candidates (-30.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	91	5	96

Merged error: 7.1b

Counts

96 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt 1/3) (cbrt 1/3))
6.1b	(pow (pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
28.9b	(cbrt (+ (* re re) (* im im)))
30.1b	(pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`cbrt-prod`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`unpow-prod-down`
12×	`pow1`
9×	`add-exp-log`
7×	`pow-unpow` `pow1/3`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`pow-exp`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `sqr-pow`
2×	`cbrt-div` `pow-pow` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `flip3-+` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 94

Calls

4 calls:

5.0ms	(* (cbrt 1/3) (cbrt 1/3))
6.0ms	(pow (pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3)))

series103.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(* (cbrt 1/3) (cbrt 1/3))
46.0ms	(pow (pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
23.0ms	(cbrt (+ (* re re) (* im im)))
34.0ms	(pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3)))

simplify47.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	357	856
1	1455	798
2	5001	732

prune224.0ms

Filtered

75 candidates to 104 candidates (-38.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	104	5	109

Merged error: 7.1b

Counts

109 → 5

regimes418.0ms

Accuracy

58.9% (9.8b remaining)

Error of 17.5b against oracle of 7.7b and baseline of 31.5b

bsearch94.0ms

Steps

Iters	Range		Point
7	3.7380171380528205e+131	2.2036190371040857e+133	4.070668110430573e+132
9	1.0024453803372812e-186	4.456042333808463e-180	3.46573922954345e-184
10	2.3367118136548073e-275	3.520865103119929e-260	1.2483708959024469e-261
8	-2.123355625183021e+93	-1.3524789121729735e+89	-2.0762121055878436e+93

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	9
1	23	9

end0.0ms

sample511.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

238.0ms

8000×

body

valid

Details

sample158.0ms

simplify3.0ms

prune3.0ms

localize6.0ms

rewrite4.0ms

series6.0ms

simplify135.0ms

prune33.0ms

localize9.0ms

rewrite20.0ms

series98.0ms

simplify107.0ms

prune110.0ms

localize15.0ms

rewrite21.0ms

series97.0ms

simplify44.0ms

prune144.0ms

localize23.0ms

rewrite21.0ms

series103.0ms

simplify47.0ms

prune224.0ms

regimes418.0ms

bsearch94.0ms

simplify1.0ms

end0.0ms

sample511.0ms

Profiling