Details

sample38.0ms

Algorithm

intervals

Results

10.0ms	191×	body	80	valid
6.0ms	21×	body	2560	valid
6.0ms	16×	body	5120	valid
2.0ms	10×	body	1280	valid
2.0ms	10×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	4×	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: 40.6b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

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:

4.0ms	(+ (* re re) (* im im))
8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
22.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5282	690

prune116.0ms

Filtered

53 candidates to 63 candidates (-18.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	7	64

Merged error: 17.4b

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)))))
7.6b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
32.8b	(sqrt (+ (* re re) (* im im)))
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

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:

15.0ms	(* (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)))
5.0ms	(sqrt (+ (* re re) (* im im)))

series24.0ms

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)))

simplify54.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	6097	1470

prune140.0ms

Filtered

72 candidates to 136 candidates (-88.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	136	7	143

Merged error: 17.4b

Counts

143 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

7.3b	(+ (* (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (fabs (cbrt (+ (* re re) (* im im)))))) (sqrt (sqrt (cbrt (+ (* re re) (* im im)))))) re)
32.8b	(sqrt (+ (* re re) (* im im)))
33.8b	(cbrt (+ (* re re) (* im im)))
33.8b	(cbrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

17.0ms	(+ (* (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (fabs (cbrt (+ (* re re) (* im im)))))) (sqrt (sqrt (cbrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (fabs (cbrt (+ (* re re) (* im im)))))) (sqrt (sqrt (cbrt (+ (* re re) (* im im)))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))
22.0ms	(cbrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4933	1054
1	4933	1054

prune119.0ms

Filtered

53 candidates to 64 candidates (-20.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	63	8	71

Merged error: 17.4b

Counts

71 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 5)
13.2b	(+ (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 5) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
32.8b	(sqrt (+ (* re re) (* im im)))
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

7.0ms	(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 5)
14.0ms	(+ (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 5) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 5)
7.0ms	(+ (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 5) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify34.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4958	998
1	4958	998

prune124.0ms

Filtered

64 candidates to 80 candidates (-25.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	80	8	88

Merged error: 17.4b

Counts

88 → 8

regimes388.0ms

Accuracy

60.1% (8.7b remaining)

Error of 26.1b against oracle of 17.4b and baseline of 39.2b

bsearch41.0ms

Steps

Iters	Range		Point
9	2.14645613255865e+90	2.4314027802128217e+95	2.4095428469624423e+95
10	-1.2880785054587291e-291	-7.401970125053545e-302	-7.479484992586778e-302

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	74
1	46	74

end0.0ms

sample1.1s

Algorithm

intervals

Results

314.0ms	5965×	body	80	valid
218.0ms	695×	body	2560	valid
124.0ms	325×	body	5120	valid
123.0ms	468×	body	1280	valid
63.0ms	317×	body	640	valid
23.0ms	142×	body	320	valid
9.0ms	88×	body	160	valid

Details

sample38.0ms

simplify3.0ms

prune6.0ms

localize14.0ms

rewrite22.0ms

series39.0ms

simplify40.0ms

prune116.0ms

localize12.0ms

rewrite41.0ms

series24.0ms

simplify54.0ms

prune140.0ms

localize20.0ms

rewrite28.0ms

series82.0ms

simplify58.0ms

prune119.0ms

localize18.0ms

rewrite29.0ms

series57.0ms

simplify34.0ms

prune124.0ms

regimes388.0ms

bsearch41.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling