Details

sample32.0ms

Algorithm

intervals

Results

9.0ms	201×	body	80	valid
7.0ms	25×	body	2560	valid
5.0ms	14×	body	5120	valid
1.0ms	4×	body	1280	valid
1.0ms	4×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune3.0ms

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: 40.6b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

1.2b	(+ (sqrt (+ (* re re) (* im im))) re)
33.4b	(sqrt (+ (* re re) (* im im)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

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

series83.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	141	198
1	358	186
2	866	182
3	2557	181
4	5001	181

prune116.0ms

Filtered

33 candidates to 29 candidates (87.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	27	6	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	7	34

Merged error: 19.2b

Counts

34 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
4.8b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
34.3b	(cbrt (+ (* re re) (* im im)))
34.3b	(cbrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 65

Calls

4 calls:

8.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
8.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
78.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
91.0ms	(cbrt (+ (* re re) (* im im)))
91.0ms	(cbrt (+ (* re re) (* im im)))

simplify43.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	323	928
1	1214	868
2	5002	841

prune297.0ms

Filtered

77 candidates to 66 candidates (85.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	5	5
Picked	1	0	1
Done	1	0	1
Total	78	6	84

Merged error: 19.2b

Counts

84 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

7.1b	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
33.4b	(sqrt (+ (* re re) (* im im)))
33.4b	(sqrt (+ (* re re) (* im im)))
33.4b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

20.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	160	641
1	431	527
2	1354	481
3	5001	477

prune258.0ms

Filtered

68 candidates to 60 candidates (88.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	67	7	74

Merged error: 19.2b

Counts

74 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

7.1b	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
33.4b	(sqrt (+ (* re re) (* im im)))
33.4b	(sqrt (+ (* re re) (* im im)))
33.4b	(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

21.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	160	641
1	431	527
2	1354	481
3	5001	477

prune290.0ms

Filtered

68 candidates to 61 candidates (89.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	67	8	75

Merged error: 19.2b

Counts

75 → 8

regimes192.0ms

Accuracy

56.5% (9.4b remaining)

Error of 27.4b against oracle of 17.9b and baseline of 39.6b

bsearch126.0ms

Steps

Iters	Range		Point
10	7.981098076133901e+52	8.549531690056054e+66	1.1231365626873932e+66
9	1.625473957011741e-208	1.8507233151258125e-202	1.3079301294629651e-207
6	6.351876487387151e-290	3.3000252034626215e-289	1.8211799526759194e-289

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	39
1	49	39

end0.0ms

sample901.0ms

Algorithm

intervals

Results

289.0ms	6044×	body	80	valid
193.0ms	703×	body	2560	valid
108.0ms	480×	body	1280	valid
94.0ms	290×	body	5120	valid
51.0ms	250×	body	640	valid
22.0ms	165×	body	320	valid
6.0ms	68×	body	160	valid

Details

sample32.0ms

simplify5.0ms

prune3.0ms

localize13.0ms

rewrite11.0ms

series83.0ms

simplify80.0ms

prune116.0ms

localize18.0ms

rewrite25.0ms

series368.0ms

simplify43.0ms

prune297.0ms

localize14.0ms

rewrite32.0ms

series156.0ms

simplify52.0ms

prune258.0ms

localize18.0ms

rewrite33.0ms

series157.0ms

simplify52.0ms

prune290.0ms

regimes192.0ms

bsearch126.0ms

simplify2.0ms

end0.0ms

sample901.0ms

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