Details

sample15.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	7	4

prune2.0ms

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: 33.2b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* re re) (* im im))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite10.0ms

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:

4.0ms	(+ (* re re) (* im im))
6.0ms	(sqrt (+ (* re re) (* im im)))

series63.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(+ (* re re) (* im im))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (47.0ms)

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

prune61.0ms

Filtered

32 candidates to 25 candidates (78.1%)

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: 8.4b

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)))))
32.2b	(cbrt (+ (* re re) (* im im)))
32.2b	(cbrt (+ (* re re) (* im im)))

rewrite24.0ms

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))))
11.0ms	(* (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)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
112.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
92.0ms	(cbrt (+ (* re re) (* im im)))
93.0ms	(cbrt (+ (* re re) (* im im)))

simplify122.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	277	855
1	1061	799
2	4305	786
3	5001	779

prune211.0ms

Filtered

86 candidates to 72 candidates (83.7%)

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: 8.4b

Counts

91 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

32.2b	(cbrt (+ (* re re) (* im im)))
32.2b	(cbrt (+ (* re re) (* im im)))
32.2b	(cbrt (+ (* re re) (* im im)))
32.2b	(cbrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

3.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (+ (* re re) (* im im)))
93.0ms	(cbrt (+ (* re re) (* im im)))
92.0ms	(cbrt (+ (* re re) (* im im)))
94.0ms	(cbrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	123	488
1	408	452
2	1386	444
3	5001	444

prune224.0ms

Filtered

64 candidates to 60 candidates (93.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	64	6	70

Merged error: 8.4b

Counts

70 → 6

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	3	3
Total	6	6

Merged error: 8.4b

Counts

6 → 6

regimes280.0ms

Accuracy

54.6% (10.7b remaining)

Error of 18.1b against oracle of 7.4b and baseline of 31.0b

bsearch106.0ms

Steps

Iters	Range		Point
9	9.092643328338922e+123	2.512579933221449e+133	2.131858430038115e+127
8	1.8262583030760354e-113	5.043517582814353e-109	1.8637666906269956e-113
9	9.929777800337937e-288	5.34670244842392e-280	4.7499823253112636e-281
9	-2.423146045177123e+82	-4.950444471151729e+75	-1.4268239453600389e+82

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	9
1	23	9

end0.0ms

sample390.0ms

Algorithm

intervals

Results

252.0ms

8000×

body

valid