Details

sample34.0ms

Algorithm

intervals

Results

8.0ms	181×	body	80	valid
7.0ms	29×	body	2560	valid
4.0ms	11×	body	5120	valid
3.0ms	17×	body	640	valid
2.0ms	10×	body	1280	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	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: 40.9b

Counts

2 → 1

localize16.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (sqrt (+ (* re re) (* im im))) re)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`*-un-lft-identity`
4×	`sqrt-prod` `add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `distribute-lft-out--`

Counts

2 → 30

Calls

2 calls:

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

series96.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(- (sqrt (+ (* re re) (* im im))) re)
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify82.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 4 (77.0ms)

Iter	Nodes	Cost
0	135	228
1	332	216
2	839	212
3	2503	211
4	5002	210

prune105.0ms

Filtered

36 candidates to 28 candidates (77.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	30	6	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	7	37

Merged error: 20.3b

Counts

37 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
8.9b	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
30.7b	(cbrt (+ (* re re) (* im im)))
30.7b	(cbrt (+ (* re re) (* im im)))

rewrite26.0ms

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`
3×	`flip3-+` `associate-l` `flip-+` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 66

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

series377.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
81.0ms	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
92.0ms	(cbrt (+ (* re re) (* im im)))
95.0ms	(cbrt (+ (* re re) (* im im)))

simplify146.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	307	930
1	1159	870
2	4797	842
3	5002	842

prune265.0ms

Filtered

78 candidates to 64 candidates (82.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	77	8	85

Merged error: 20.3b

Counts

85 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

10.6b	(- (* (fabs (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im)))))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
29.7b	(sqrt (+ (* re re) (* im im)))
29.7b	(sqrt (+ (* re re) (* im im)))
30.7b	(cbrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

9.0ms	(- (* (fabs (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im)))))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* (fabs (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im)))))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
94.0ms	(cbrt (+ (* re re) (* im im)))

simplify90.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	259	719
1	892	652
2	2925	631
3	5001	629

prune278.0ms

Filtered

67 candidates to 58 candidates (86.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	67	8	75

Merged error: 20.3b

Counts

75 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

30.7b	(cbrt (+ (* re re) (* im im)))
30.7b	(cbrt (+ (* re re) (* im im)))
30.7b	(cbrt (+ (* re re) (* im im)))
30.7b	(cbrt (+ (* re re) (* im im)))

rewrite16.0ms

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)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (+ (* re re) (* im im)))
92.0ms	(cbrt (+ (* re re) (* im im)))
93.0ms	(cbrt (+ (* re re) (* im im)))
93.0ms	(cbrt (+ (* re re) (* im im)))

simplify51.0ms

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

prune305.0ms

Filtered

64 candidates to 60 candidates (93.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	64	8	72

Merged error: 20.3b

Counts

72 → 8

regimes456.0ms

Accuracy

55.9% (9.2b remaining)

Error of 26.8b against oracle of 17.6b and baseline of 38.5b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	41
1	46	41

end0.0ms

sample873.0ms

Algorithm

intervals

Results

280.0ms	6036×	body	80	valid
192.0ms	715×	body	2560	valid
97.0ms	458×	body	1280	valid
93.0ms	305×	body	5120	valid
44.0ms	257×	body	640	valid
18.0ms	145×	body	320	valid
7.0ms	84×	body	160	valid

Details

sample34.0ms

simplify8.0ms

prune3.0ms

localize16.0ms

rewrite15.0ms

series96.0ms

simplify82.0ms

prune105.0ms

localize18.0ms

rewrite26.0ms

series377.0ms

simplify146.0ms

prune265.0ms

localize18.0ms

rewrite21.0ms

series243.0ms

simplify90.0ms

prune278.0ms

localize22.0ms

rewrite16.0ms

series370.0ms

simplify51.0ms

prune305.0ms

regimes456.0ms

bsearch2.0ms

simplify1.0ms

end0.0ms

sample873.0ms

Profiling