Details

analyze339.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

sample34.0ms

Algorithm

intervals

Results

10.0ms	199×	body	80	valid
6.0ms	16×	body	1280	valid
6.0ms	20×	body	2560	valid
2.0ms	9×	body	640	valid
1.0ms	4×	body	5120	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: 37.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

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

series43.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
25.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify29.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5008	690

prune130.0ms

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: 16.6b

Counts

64 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sqrt (* (+ re (sqrt (+ (* re re) (* im im)))) 2.0)) 3)
0.9b	(+ re (sqrt (+ (* re re) (* im im))))
15.6b	(cbrt (pow (sqrt (* (+ re (sqrt (+ (* re re) (* im im)))) 2.0)) 3))
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
13×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
9×	`pow1`
8×	`unpow-prod-down` `cube-prod`
7×	`sqrt-prod`
6×	`sqrt-div` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`cube-div` `pow-pow` `flip3-+` `associate-*l/` `flip-+`
3×	`pow-unpow` `sqrt-pow1`
2×	`cube-mult` `cbrt-div` `pow1/2` `unpow3` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `pow1/3` `pow-prod-down` `pow-exp` `sum-log` `sqrt-pow2` `rem-cbrt-cube` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 83

Calls

4 calls:

8.0ms	(pow (sqrt (* (+ re (sqrt (+ (* re re) (* im im)))) 2.0)) 3)
6.0ms	(+ re (sqrt (+ (* re re) (* im im))))
4.0ms	(cbrt (pow (sqrt (* (+ re (sqrt (+ (* re re) (* im im)))) 2.0)) 3))
4.0ms	(sqrt (+ (* re re) (* im im)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (sqrt (* (+ re (sqrt (+ (* re re) (* im im)))) 2.0)) 3)
7.0ms	(+ re (sqrt (+ (* re re) (* im im))))
25.0ms	(cbrt (pow (sqrt (* (+ re (sqrt (+ (* re re) (* im im)))) 2.0)) 3))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4957	1400
1	4957	1400

prune140.0ms

Filtered

62 candidates to 95 candidates (-53.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	94	8	102

Merged error: 16.6b

Counts

102 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.0b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
28.2b	(sqrt (+ (* re re) (* im im)))
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite46.0ms

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)))))
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)))

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)))

simplify70.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4944	1470
1	4944	1470

prune143.0ms

Filtered

73 candidates to 136 candidates (-86.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	136	8	144

Merged error: 16.6b

Counts

144 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ re (sqrt (+ (* re re) (* im im))))
2.9b	(exp (* 3 (log (sqrt (* (+ re (sqrt (+ (* re re) (* im im)))) 2.0)))))
15.6b	(cbrt (exp (* 3 (log (sqrt (* (+ re (sqrt (+ (* re re) (* im im)))) 2.0))))))
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod` `exp-sum`
12×	`*-un-lft-identity`
11×	`cbrt-prod` `add-sqr-sqrt`
10×	`add-cube-cbrt`
8×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp`
7×	`sqrt-prod`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `exp-prod` `exp-to-pow` `sqrt-pow1` `pow1/2` `pow1/3` `sum-log` `rem-exp-log` `distribute-lft-out`

Counts

4 → 64

Calls

4 calls:

6.0ms	(+ re (sqrt (+ (* re re) (* im im))))
3.0ms	(exp (* 3 (log (sqrt (* (+ re (sqrt (+ (* re re) (* im im)))) 2.0)))))
4.0ms	(cbrt (exp (* 3 (log (sqrt (* (+ re (sqrt (+ (* re re) (* im im)))) 2.0))))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ re (sqrt (+ (* re re) (* im im))))
64.0ms	(exp (* 3 (log (sqrt (* (+ re (sqrt (+ (* re re) (* im im)))) 2.0)))))
23.0ms	(cbrt (exp (* 3 (log (sqrt (* (+ re (sqrt (+ (* re re) (* im im)))) 2.0))))))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify38.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4970	1063
1	4970	1063

prune108.0ms

Filtered

52 candidates to 76 candidates (-46.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	76	8	84

Merged error: 16.6b

Counts

84 → 8

regimes257.0ms

Accuracy

41.8% (12.5b remaining)

Error of 29.3b against oracle of 16.8b and baseline of 38.3b

bsearch83.0ms

Steps

Iters	Range	Point
10	3.998855284750248e+63	6.121078258950455e+74	6.76894866017109e+68
9	1.7755267273505142e-156	1.171250964795389e-149	2.1109892546767475e-156
8	-3.0771878019732518e-201	-7.920789041027829e-206	-2.8332709859495543e-201

Iters

Range

Point

3.998855284750248e+63

6.121078258950455e+74

6.76894866017109e+68

1.7755267273505142e-156

1.171250964795389e-149

2.1109892546767475e-156

-3.0771878019732518e-201

-7.920789041027829e-206

-2.8332709859495543e-201

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	74
1	58	74

end0.0ms

sample935.0ms

Algorithm

intervals

Results

297.0ms	6055×	body	80	valid
203.0ms	721×	body	2560	valid
112.0ms	477×	body	1280	valid
93.0ms	264×	body	5120	valid
55.0ms	277×	body	640	valid
18.0ms	130×	body	320	valid
7.0ms	76×	body	160	valid

Details

analyze339.0ms

sample34.0ms

simplify3.0ms

prune6.0ms

localize11.0ms

rewrite24.0ms

series43.0ms

simplify29.0ms

prune130.0ms

localize14.0ms

rewrite24.0ms

series101.0ms

simplify52.0ms

prune140.0ms

localize13.0ms

rewrite46.0ms

series25.0ms

simplify70.0ms

prune143.0ms

localize19.0ms

rewrite19.0ms

series100.0ms

simplify38.0ms

prune108.0ms

regimes257.0ms

bsearch83.0ms

simplify2.0ms

end0.0ms

sample935.0ms

Profiling