Details

sample12.0ms

Algorithm

intervals

Results

5.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize5.0ms

Local error

Found 1 expressions with local error:

31.8b

(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)))

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

(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

prune45.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (cbrt (+ (* re re) (* im im))))
0.2b	(* (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)))

rewrite21.0ms

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)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
105.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
91.0ms	(cbrt (+ (* re re) (* im im)))
94.0ms	(cbrt (+ (* re re) (* im im)))

simplify128.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	277	853
1	1072	799
2	4426	786
3	5002	779

prune235.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.4b

localize14.0ms

Local error

Found 4 expressions with local error:

32.8b	(cbrt (+ (* re re) (* im im)))
32.8b	(cbrt (+ (* re re) (* im im)))
32.8b	(cbrt (+ (* re re) (* im im)))
32.8b	(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)))
4.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (+ (* re re) (* im im)))
92.0ms	(cbrt (+ (* re re) (* im im)))
90.0ms	(cbrt (+ (* re re) (* im im)))
89.0ms	(cbrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (12.0ms)

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

prune241.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 8.4b

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

5 alts after pruning (2 fresh and 3 done)

Merged error: 8.4b

regimes230.0ms

Accuracy

58.5% (9.8b remaining)

Error of 17.3b against oracle of 7.5b and baseline of 31.1b

bsearch48.0ms

Steps

Iters	Range		Point
9	1.3035143797826932e+113	1.0263498879426634e+121	9.175373788887837e+116
9	-4.331403552570957e+63	-1.1145548392722344e+57	-3.6980740601030615e+63

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	5
1	17	5

end0.0ms

sample291.0ms

Algorithm

intervals

Results

172.0ms

8000×

body

valid