Details

analyze87.0ms

Algorithm: search

sample14.0ms

Algorithm

intervals

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: 33.9b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* re re) (* im im))
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

3.0ms	(+ (* re re) (* im im))
4.0ms	(sqrt (+ (* re re) (* im im)))

series13.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(+ (* re re) (* im im))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	125	177
1	530	163
2	1540	163
3	5001	162

prune45.0ms

Filtered

25 candidates to 32 candidates (-28.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	5	33

Merged error: 10.1b

Counts

33 → 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)))))
32.8b	(cbrt (+ (* re re) (* im im)))
32.8b	(cbrt (+ (* re re) (* im im)))

rewrite22.0ms

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))))
8.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
3.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
34.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
21.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))

simplify108.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (95.0ms)

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

prune118.0ms

Filtered

72 candidates to 86 candidates (-19.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	85	6	91

Merged error: 10.1b

Counts

91 → 6

localize16.0ms

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)))))
32.8b	(cbrt (+ (* re re) (* im im)))
34.8b	(pow (+ (* re re) (* im im)) 1/3)

rewrite22.0ms

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))))
8.0ms	(* (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)

series99.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
36.0ms	(* (fabs (pow (+ (* re re) (* im im)) 1/3)) (sqrt (cbrt (+ (* re re) (* im im)))))
21.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(pow (+ (* re re) (* im im)) 1/3)

simplify43.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (33.0ms)

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

prune142.0ms

Filtered

69 candidates to 91 candidates (-31.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	91	6	97

Merged error: 10.1b

Counts

97 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt 1/3) (cbrt 1/3))
6.3b	(pow (pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
32.8b	(cbrt (+ (* re re) (* im im)))
33.8b	(pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3)))

rewrite22.0ms

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

series106.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(* (cbrt 1/3) (cbrt 1/3))
50.0ms	(pow (pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
21.0ms	(cbrt (+ (* re re) (* im im)))
35.0ms	(pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3)))

simplify48.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (38.0ms)

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

prune216.0ms

Filtered

75 candidates to 104 candidates (-38.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	104	6	110

Merged error: 10.1b

Counts

110 → 6

regimes504.0ms

Accuracy

59.8% (9.5b remaining)

Error of 16.9b against oracle of 7.4b and baseline of 31.0b

bsearch48.0ms

Steps

Iters	Range		Point
6	5.693365055063027e+149	2.5572264153950414e+150	5.762764879306503e+149
4	-2.926845128760278e+149	-1.699897758245427e+149	-1.8227820349801547e+149

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	5
1	17	5

end0.0ms

analyze90.0ms

Algorithm: search

sample561.0ms

Algorithm

intervals

Results

436.0ms

8000×

body

valid

Details

analyze87.0ms

sample14.0ms

simplify3.0ms

prune3.0ms

localize5.0ms

rewrite7.0ms

series13.0ms

simplify46.0ms

prune45.0ms

localize9.0ms

rewrite22.0ms

series97.0ms

simplify108.0ms

prune118.0ms

localize16.0ms

rewrite22.0ms

series99.0ms

simplify43.0ms

prune142.0ms

localize27.0ms

rewrite22.0ms

series106.0ms

simplify48.0ms

prune216.0ms

regimes504.0ms

bsearch48.0ms

simplify1.0ms

end0.0ms

analyze90.0ms

sample561.0ms

Profiling