Details

sample21.0ms

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

Filtered

1 candidates to 0 candidates (100.0%)

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: 28.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* re re) (* im im))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite8.0ms

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

series78.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ (* re re) (* im im))
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (46.0ms)

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

prune76.0ms

Filtered

32 candidates to 25 candidates (21.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	27	5	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	6	33

Merged error: 7.8b

Counts

33 → 6

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (* re re) (* im im))))
0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

4.0ms	(sqrt (sqrt (+ (* re re) (* im im))))
14.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt (sqrt (+ (* re re) (* im im))))
42.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
44.0ms	(sqrt (+ (* re re) (* im im)))
46.0ms	(sqrt (+ (* re re) (* im im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	266	1058
1	1073	988
2	5001	967

prune268.0ms

Filtered

146 candidates to 76 candidates (47.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	146	6	152

Merged error: 7.8b

Counts

152 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
5.6b	(exp (log (sqrt (+ (* re re) (* im im)))))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 48

Calls

3 calls:

4.0ms	(+ (* re re) (* im im))
5.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
3.0ms	(sqrt (+ (* re re) (* im im)))

series122.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (* re re) (* im im))
43.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
46.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	172	330
1	601	313
2	1676	304
3	5001	296

prune149.0ms

Filtered

57 candidates to 38 candidates (33.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	55	8	63

Merged error: 7.8b

Counts

63 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

5.8b	(pow (exp (* (cbrt (log (sqrt (+ (* re re) (* im im))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`pow-unpow` `sqrt-prod`
6×	`cbrt-prod` `sqrt-div`
5×	`add-log-exp`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube`
3×	`unpow-prod-down` `rem-sqrt-square` `pow-pow` `flip3-+` `log-pow` `flip-+`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow-exp` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

4.0ms	(pow (exp (* (cbrt (log (sqrt (+ (* re re) (* im im))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(pow (exp (* (cbrt (log (sqrt (+ (* re re) (* im im))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))
45.0ms	(sqrt (+ (* re re) (* im im)))
43.0ms	(sqrt (+ (* re re) (* im im)))
45.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	189	925
1	499	852
2	1541	846
3	5002	842

prune295.0ms

Filtered

82 candidates to 63 candidates (23.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	82	8	90

Merged error: 7.8b

Counts

90 → 8

regimes560.0ms

Accuracy

58.1% (9.8b remaining)

Error of 17.6b against oracle of 7.8b and baseline of 31.2b

bsearch52.0ms

Steps

Iters	Range		Point
5	2.2866843337900248e+77	5.514542683406611e+77	4.325223030489154e+77
8	-3.719641692260901e+158	-1.2498419091925624e+154	-1.269258234578637e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	5
1	17	5

end0.0ms

sample426.0ms

Algorithm

intervals

Results

223.0ms

8000×

body

valid

Details

sample21.0ms

simplify3.0ms

prune3.0ms

localize6.0ms

rewrite8.0ms

series78.0ms

simplify49.0ms

prune76.0ms

localize8.0ms

rewrite30.0ms

series245.0ms

simplify48.0ms

prune268.0ms

localize10.0ms

rewrite13.0ms

series122.0ms

simplify51.0ms

prune149.0ms

localize19.0ms

rewrite16.0ms

series463.0ms

simplify53.0ms

prune295.0ms

regimes560.0ms

bsearch52.0ms

simplify1.0ms

end0.0ms

sample426.0ms

Profiling