Details

analyze322.0ms

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

sample35.0ms

Algorithm

intervals

Results

9.0ms	194×	body	80	valid
5.0ms	20×	body	2560	valid
4.0ms	12×	body	5120	valid
4.0ms	4×	body	320	valid
3.0ms	13×	body	1280	valid
2.0ms	10×	body	640	valid
0.0ms	3×	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: 35.7b

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)))
1.3b	(+ (sqrt (+ (* re re) (* im im))) re)
27.6b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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))
7.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series42.0ms

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)))

simplify39.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5151	682

prune123.0ms

Filtered

52 candidates to 63 candidates (-21.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	55	8	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	9	64

Merged error: 16.7b

Counts

64 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
6.2b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
28.6b	(cbrt (+ (* re re) (* im im)))
28.6b	(cbrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

8.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
8.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series103.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
28.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
22.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5235	1420

prune146.0ms

Filtered

65 candidates to 77 candidates (-18.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	76	10	86

Merged error: 16.7b

Counts

86 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

28.6b	(cbrt (+ (* re re) (* im im)))
28.6b	(cbrt (+ (* re re) (* im im)))
28.6b	(cbrt (+ (* re re) (* im im)))
28.6b	(cbrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))
23.0ms	(cbrt (+ (* re re) (* im im)))

simplify36.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5263	772

prune136.0ms

Filtered

56 candidates to 64 candidates (-14.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	64	10	74

Merged error: 16.7b

Counts

74 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
15.0b	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
27.6b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

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:

10.0ms	(sqrt (* 2.0 (+ (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
9.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify34.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4936	784
1	4936	784

prune93.0ms

Filtered

54 candidates to 74 candidates (-37.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	69	5	74
Fresh	0	7	7
Picked	1	0	1
Done	1	1	2
Total	71	13	84

Merged error: 16.6b

Counts

84 → 13

regimes862.0ms

Accuracy

57.5% (9.1b remaining)

Error of 26.5b against oracle of 17.4b and baseline of 38.9b

bsearch54.0ms

Steps

Iters	Range		Point
9	8.588851200611536e+67	1.1304504666992013e+75	1.1095515437686829e+75
7	-1.7910444071393555e-308	1.5012133835451467e-307	-3.4246941374715e-310

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	51
1	36	51

end0.0ms

analyze327.0ms

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

sample909.0ms

Algorithm

intervals

Results

294.0ms	6028×	body	80	valid
194.0ms	712×	body	2560	valid
111.0ms	494×	body	1280	valid
89.0ms	272×	body	5120	valid
51.0ms	264×	body	640	valid
20.0ms	152×	body	320	valid
7.0ms	78×	body	160	valid

Details

analyze322.0ms

sample35.0ms

simplify3.0ms

prune6.0ms

localize11.0ms

rewrite23.0ms

series42.0ms

simplify39.0ms

prune123.0ms

localize14.0ms

rewrite24.0ms

series103.0ms

simplify47.0ms

prune146.0ms

localize21.0ms

rewrite16.0ms

series84.0ms

simplify36.0ms

prune136.0ms

localize15.0ms

rewrite30.0ms

series43.0ms

simplify34.0ms

prune93.0ms

regimes862.0ms

bsearch54.0ms

simplify1.0ms

end0.0ms

analyze327.0ms

sample909.0ms

Profiling