Details

sample13.0ms

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: 36.7b

localize5.0ms

Local error

Found 1 expressions with local error:

34.5b

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

rewrite8.0ms

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:

8.0ms

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

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

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

simplify134.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 5 (131.0ms)

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: 10.6b

localize9.0ms

Local error

Found 2 expressions with local error:

5.9b	(exp (log (sqrt (+ (* re re) (* im im)))))
34.5b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

13.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
8.0ms	(sqrt (+ (* re re) (* im im)))

series65.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
33.0ms	(sqrt (+ (* re re) (* im im)))

simplify150.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 5 (146.0ms)

Iter	Nodes	Cost
0	136	253
1	280	247
2	583	238
3	1387	232
4	4698	232
5	5001	228

prune93.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.6b

localize15.0ms

Local error

Found 2 expressions with local error:

6.3b	(pow E (log (sqrt (+ (* re re) (* im im)))))
34.5b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `unpow-prod-up` `pow-unpow` `log-prod` `sqrt-prod`
4×	`sqrt-div`
3×	`add-exp-log` `unpow-prod-down` `log-pow`
2×	`log-div` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `add-cbrt-cube` `flip-+` `pow-sub` `add-log-exp`
1×	`pow-to-exp` `rem-sqrt-square` `e-exp-1` `pow-pow` `sqr-pow`

Counts

2 → 44

Calls

2 calls:

10.0ms	(pow E (log (sqrt (+ (* re re) (* im im)))))
8.0ms	(sqrt (+ (* re re) (* im im)))

series314.0ms

Counts

2 → 6

Calls

2 calls:

278.0ms	(pow E (log (sqrt (+ (* re re) (* im im)))))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	205	384
1	542	372
2	1697	365
3	5001	363

prune120.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.6b

localize32.0ms

Local error

Found 4 expressions with local error:

17.2b	(sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
35.5b	(cbrt (+ (* re re) (* im im)))
35.5b	(cbrt (+ (* re re) (* im im)))
35.5b	(cbrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
12×	`pow1`
9×	`cbrt-prod` `sqrt-pow1` `flip3-+` `pow1/3` `flip-+`
8×	`sqrt-div`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `frac-times` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 66

Calls

4 calls:

18.0ms	(sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
5.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
87.0ms	(cbrt (+ (* re re) (* im im)))
86.0ms	(cbrt (+ (* re re) (* im im)))
89.0ms	(cbrt (+ (* re re) (* im im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	183	671
1	555	635
2	1969	629
3	5003	626

prune306.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.6b

regimes296.0ms

Accuracy

57.7% (10.0b remaining)

Error of 17.8b against oracle of 7.8b and baseline of 31.5b

bsearch42.0ms

Steps

Iters	Range		Point
10	5.021239776809263e+39	2.034575374228523e+56	1.8659245901416584e+56
8	-2.505330959308098e+109	-9.022777940030645e+106	-1.3002851623049085e+108

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	5
1	17	5

end0.0ms

sample332.0ms

Algorithm

intervals

Results

162.0ms

8000×

body

valid