Details

analyze338.0ms

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

sample79.0ms

Algorithm

intervals

Results

8.0ms	192×	body	80	valid
8.0ms	29×	body	2560	valid
3.0ms	13×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	2×	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

prune7.0ms

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

localize12.0ms

Local error

Found 3 expressions with local error:

6.1b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
8.1b	(+ (sqrt (+ (* re re) (* im im))) re)
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

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)))

series38.0ms

Counts

3 → 9

Calls

3 calls:

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)))

simplify49.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4936	551
1	4936	551

prune109.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	43	6	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	6	50

Merged error: 20.6b

Counts

50 → 6

localize52.0ms

Local error

Found 4 expressions with local error:

5.9b	(exp (log (sqrt (+ (* re re) (* im im)))))
6.1b	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
8.1b	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

6.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
11.0ms	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
10.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify41.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4974	784
1	4974	784

prune132.0ms

Filtered

55 candidates to 74 candidates (-34.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	69	5	74
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	70	10	80

Merged error: 20.4b

Counts

80 → 10

localize183.0ms

Local error

Found 4 expressions with local error:

6.1b	(sqrt (* 2.0 (+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)))
6.2b	(pow E (log (sqrt (+ (* re re) (* im im)))))
8.1b	(+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

14.0ms	(sqrt (* 2.0 (+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)))
6.0ms	(pow E (log (sqrt (+ (* re re) (* im im)))))
11.0ms	(+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (* 2.0 (+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)))
19.0ms	(pow E (log (sqrt (+ (* re re) (* im im)))))
16.0ms	(+ (pow E (log (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5028	1181

prune152.0ms

Filtered

62 candidates to 81 candidates (-30.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	80	11	91

Merged error: 20.4b

Counts

91 → 11

localize333.0ms

Local error

Found 4 expressions with local error:

6.1b	(sqrt (* 2.0 (+ (* (pow E (* 2 (log (cbrt (sqrt (+ (* re re) (* im im))))))) (pow E (log (cbrt (sqrt (+ (* re re) (* im im))))))) re)))
8.1b	(+ (* (pow E (* 2 (log (cbrt (sqrt (+ (* re re) (* im im))))))) (pow E (log (cbrt (sqrt (+ (* re re) (* im im))))))) re)
31.0b	(sqrt (+ (* re re) (* im im)))
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

20.0ms	(sqrt (* 2.0 (+ (* (pow E (* 2 (log (cbrt (sqrt (+ (* re re) (* im im))))))) (pow E (log (cbrt (sqrt (+ (* re re) (* im im))))))) re)))
21.0ms	(+ (* (pow E (* 2 (log (cbrt (sqrt (+ (* re re) (* im im))))))) (pow E (log (cbrt (sqrt (+ (* re re) (* im im))))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(sqrt (+ (* re re) (* im im)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt (* 2.0 (+ (* (pow E (* 2 (log (cbrt (sqrt (+ (* re re) (* im im))))))) (pow E (log (cbrt (sqrt (+ (* re re) (* im im))))))) re)))
56.0ms	(+ (* (pow E (* 2 (log (cbrt (sqrt (+ (* re re) (* im im))))))) (pow E (log (cbrt (sqrt (+ (* re re) (* im im))))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4962	994
1	4962	994

prune125.0ms

Filtered

56 candidates to 66 candidates (-17.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	65	12	77

Merged error: 20.4b

Counts

77 → 12

regimes360.0ms

Accuracy

41.2% (13.7b remaining)

Error of 30.7b against oracle of 17.0b and baseline of 40.3b

bsearch61.0ms

Steps

Iters	Range	Point
1	7.359661053394594e-118	7.684464845587028e-118	7.4408620014427016e-118
8	-6.1090312942086945e-61	-4.857223795115068e-65	-8.818158973525325e-65
9	-2.202823131635953e+165	-4.64943276953332e+157	-4.7178184386274894e+157

Iters

Range

Point

7.359661053394594e-118

7.684464845587028e-118

7.4408620014427016e-118

-6.1090312942086945e-61

-4.857223795115068e-65

-8.818158973525325e-65

-2.202823131635953e+165

-4.64943276953332e+157

-4.7178184386274894e+157

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	55
1	48	55

end0.0ms

sample1.4s

Algorithm

intervals

Results

270.0ms	6077×	body	80	valid
195.0ms	721×	body	2560	valid
93.0ms	415×	body	1280	valid
92.0ms	271×	body	5120	valid
50.0ms	284×	body	640	valid
22.0ms	160×	body	320	valid
7.0ms	72×	body	160	valid

Details

analyze338.0ms

sample79.0ms

simplify3.0ms

prune7.0ms

localize12.0ms

rewrite20.0ms

series38.0ms

simplify49.0ms

prune109.0ms

localize52.0ms

rewrite34.0ms

series44.0ms

simplify41.0ms

prune132.0ms

localize183.0ms

rewrite37.0ms

series65.0ms

simplify57.0ms

prune152.0ms

localize333.0ms

rewrite51.0ms

series123.0ms

simplify62.0ms

prune125.0ms

regimes360.0ms

bsearch61.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling