Details

sample45.0ms

Algorithm

intervals

Results

12.0ms	193×	body	80	valid
7.0ms	19×	body	2560	valid
5.0ms	12×	body	5120	valid
5.0ms	16×	body	1280	valid
2.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 38.5b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

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:

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

series13.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify72.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	6207	327

prune271.0ms

Filtered

28 candidates to 33 candidates (-17.9%)

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: 18.9b

Counts

34 → 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)))))
8.5b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.9b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

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:

16.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
15.0ms	(+ (* (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)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
9.0ms	(sqrt (+ (* re re) (* im im)))

simplify71.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4944	1470
1	4944	1470

prune139.0ms

Filtered

70 candidates to 136 candidates (-94.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	135	8	143

Merged error: 18.9b

Counts

143 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
10.7b	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
29.9b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
11×	`sqrt-pow1`
10×	`pow1` `sqrt-div`
7×	`pow-pow`
6×	`add-log-exp`
5×	`add-exp-log` `pow1/2` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow-unpow`
2×	`cube-div` `rem-sqrt-square`
1×	`+-commutative` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `sum-log` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

8.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
20.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
8.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5149	1268

prune164.0ms

Filtered

65 candidates to 103 candidates (-58.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	102	9	111

Merged error: 18.9b

Counts

111 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

11.0b	(+ (* (* (pow (fabs (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) 3) (pow (sqrt (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) 3)) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
29.9b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

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:

24.0ms	(+ (* (* (pow (fabs (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) 3) (pow (sqrt (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) 3)) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* (* (pow (fabs (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) 3) (pow (sqrt (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) 3)) (sqrt (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)))

simplify51.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5062	1120

prune153.0ms

Filtered

57 candidates to 68 candidates (-19.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	68	9	77

Merged error: 18.9b

Counts

77 → 9

regimes760.0ms

Accuracy

57.6% (8.8b remaining)

Error of 26.8b against oracle of 18.0b and baseline of 38.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	74
1	46	74

end0.0ms

sample960.0ms

Algorithm

intervals

Results

282.0ms	6057×	body	80	valid
187.0ms	671×	body	2560	valid
110.0ms	491×	body	1280	valid
92.0ms	268×	body	5120	valid
50.0ms	289×	body	640	valid
23.0ms	155×	body	320	valid
6.0ms	69×	body	160	valid

Details

sample45.0ms

simplify3.0ms

prune6.0ms

localize10.0ms

rewrite12.0ms

series13.0ms

simplify72.0ms

prune271.0ms

localize12.0ms

rewrite44.0ms

series29.0ms

simplify71.0ms

prune139.0ms

localize16.0ms

rewrite40.0ms

series52.0ms

simplify44.0ms

prune164.0ms

localize24.0ms

rewrite42.0ms

series65.0ms

simplify51.0ms

prune153.0ms

regimes760.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample960.0ms

Profiling