Details

sample35.0ms

Algorithm

intervals

Results

9.0ms	187×	body	80	valid
8.0ms	29×	body	2560	valid
4.0ms	18×	body	1280	valid
2.0ms	6×	body	5120	valid
2.0ms	11×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify4.0ms

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

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: 39.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(+ (sqrt (+ (* re re) (* im im))) re)
0.5b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

7.0ms	(+ (* re re) (* im im))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
3.0ms	(sqrt (+ (* re re) (* im im)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
23.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify89.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	277	428
1	1024	399
2	3458	393
3	5002	391

prune113.0ms

Filtered

52 candidates to 63 candidates (-21.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Merged error: 19.7b

Counts

64 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
9.5b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`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` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

17.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
13.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify46.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	267	1096
1	974	974
2	5001	950

prune133.0ms

Filtered

73 candidates to 136 candidates (-86.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	134	9	143

Merged error: 19.7b

Counts

143 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

13.6b	(+ (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im))))))) re)
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

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:

22.0ms	(+ (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (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)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im))))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify69.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	170	713
1	540	616
2	2170	587
3	5002	584

prune133.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	68	9	77

Merged error: 19.7b

Counts

77 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

15.3b	(+ (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))))) re)
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

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:

23.0ms	(+ (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (exp (log (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)))

series28.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify69.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	174	749
1	554	638
2	2189	607
3	5001	604

prune120.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	68	9	77

Merged error: 19.7b

Counts

77 → 9

regimes698.0ms

Accuracy

54.1% (9.6b remaining)

Error of 27.6b against oracle of 18.0b and baseline of 39.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	36
1	38	36

end0.0ms

sample966.0ms

Algorithm

intervals

Results

277.0ms	6030×	body	80	valid
202.0ms	700×	body	2560	valid
114.0ms	488×	body	1280	valid
91.0ms	280×	body	5120	valid
49.0ms	278×	body	640	valid
20.0ms	149×	body	320	valid
7.0ms	75×	body	160	valid

Details

sample35.0ms

simplify4.0ms

prune3.0ms

localize10.0ms

rewrite26.0ms

series40.0ms

simplify89.0ms

prune113.0ms

localize12.0ms

rewrite42.0ms

series25.0ms

simplify46.0ms

prune133.0ms

localize20.0ms

rewrite34.0ms

series25.0ms

simplify69.0ms

prune133.0ms

localize24.0ms

rewrite35.0ms

series28.0ms

simplify69.0ms

prune120.0ms

regimes698.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample966.0ms

Profiling