Details

sample37.0ms

Algorithm

intervals

Results

13.0ms	200×	body	80	valid
7.0ms	22×	body	2560	valid
4.0ms	18×	body	1280	valid
2.0ms	5×	body	5120	valid
1.0ms	5×	body	640	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	320	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 (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: 33.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
26.2b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 38

Calls

3 calls:

4.0ms	(+ (* re re) (* im im))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series18.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* re re) (* im im))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	178	275
1	689	252
2	2017	248
3	5001	246

prune85.0ms

Filtered

47 candidates to 38 candidates (19.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	42	5	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	6	48

Merged error: 18.5b

Counts

48 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
5.7b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
27.2b	(cbrt (+ (* re re) (* im im)))
27.2b	(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)))

series104.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
28.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
20.0ms	(cbrt (+ (* re re) (* im im)))
23.0ms	(cbrt (+ (* re re) (* im im)))

simplify124.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	355	1000
1	1235	940
2	4815	899
3	5002	885

prune134.0ms

Filtered

77 candidates to 66 candidates (14.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	76	7	83

Merged error: 18.5b

Counts

83 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

4.7b	(exp (log (+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)))
5.7b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
27.2b	(cbrt (+ (* re re) (* im im)))
27.2b	(cbrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

9.0ms	(exp (log (+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)))
8.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series99.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(exp (log (+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)))
28.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
20.0ms	(cbrt (+ (* re re) (* im im)))
23.0ms	(cbrt (+ (* re re) (* im im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	328	964
1	1014	870
2	3169	799
3	5001	777

prune159.0ms

Filtered

66 candidates to 61 candidates (7.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	66	7	73

Merged error: 18.5b

Counts

73 → 7

localize33.0ms

Local error

Found 4 expressions with local error:

27.2b	(cbrt (+ (* re re) (* im im)))
27.2b	(cbrt (+ (* re re) (* im im)))
27.2b	(cbrt (+ (* re re) (* im im)))
27.2b	(cbrt (+ (* re re) (* im im)))

rewrite17.0ms

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:

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

series84.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (+ (* re re) (* im im)))
22.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	151	560
1	426	524
2	1225	500
3	5002	468

prune133.0ms

Filtered

64 candidates to 56 candidates (12.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	64	7	71

Merged error: 18.5b

Counts

71 → 7

regimes650.0ms

Accuracy

55.2% (9.6b remaining)

Error of 27.3b against oracle of 17.7b and baseline of 39.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	32
1	38	32

end0.0ms

sample974.0ms

Algorithm

intervals

Results

283.0ms	6002×	body	80	valid
188.0ms	694×	body	2560	valid
117.0ms	505×	body	1280	valid
105.0ms	319×	body	5120	valid
44.0ms	250×	body	640	valid
20.0ms	149×	body	320	valid
7.0ms	81×	body	160	valid

Details

sample37.0ms

simplify5.0ms

prune3.0ms

localize10.0ms

rewrite15.0ms

series18.0ms

simplify61.0ms

prune85.0ms

localize14.0ms

rewrite25.0ms

series104.0ms

simplify124.0ms

prune134.0ms

localize18.0ms

rewrite26.0ms

series99.0ms

simplify87.0ms

prune159.0ms

localize33.0ms

rewrite17.0ms

series84.0ms

simplify45.0ms

prune133.0ms

regimes650.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample974.0ms

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