Details

analyze335.0ms

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

9.0ms	32×	body	2560	valid
9.0ms	185×	body	80	valid
3.0ms	14×	body	1280	valid
2.0ms	7×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	6×	body	320	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

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: 40.4b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
29.7b	(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:

23.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
9.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4936	551
1	4936	551

prune128.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	39	10	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	10	50

Merged error: 17.6b

Counts

50 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ re (sqrt (+ (* re re) (* im im)))))
0.3b	(* (sqrt 2.0) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))
0.8b	(+ re (sqrt (+ (* re re) (* im im))))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

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

series52.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (+ re (sqrt (+ (* re re) (* im im)))))
24.0ms	(* (sqrt 2.0) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))
7.0ms	(+ re (sqrt (+ (* re re) (* im im))))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4941	1162
1	4941	1162

prune141.0ms

Filtered

67 candidates to 88 candidates (-31.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	87	11	98

Merged error: 17.6b

Counts

98 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
6.1b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
30.6b	(cbrt (+ (* re re) (* im im)))
30.6b	(cbrt (+ (* re re) (* im im)))

rewrite26.0ms

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)
4.0ms	(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)))))
30.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
20.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5028	1392

prune146.0ms

Filtered

65 candidates to 77 candidates (-18.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	77	11	88

Merged error: 17.6b

Counts

88 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

9.8b	(+ (* (fabs (* (sqrt (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
30.6b	(cbrt (+ (* re re) (* im im)))
30.6b	(cbrt (+ (* re re) (* im im)))
30.6b	(cbrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

9.0ms	(+ (* (fabs (* (sqrt (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series92.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* (fabs (* (sqrt (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
23.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4932	910
1	4932	910

prune96.0ms

Filtered

50 candidates to 62 candidates (-24.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	62	11	73

Merged error: 17.6b

Counts

73 → 11

regimes348.0ms

Accuracy

57.2% (9.4b remaining)

Error of 26.8b against oracle of 17.4b and baseline of 39.4b

bsearch49.0ms

Steps

Iters	Range	Point
7	1.0545712605176805e+135	7.93619059076622e+136	3.4473385511353346e+135
8	1.8755626920562477e-255	1.4081474353677686e-251	2.9058779586404625e-253
9	-6.419132125800359e-131	-1.2340554909025647e-137	-1.2574376283715415e-137

Iters

Range

Point

1.0545712605176805e+135

7.93619059076622e+136

3.4473385511353346e+135

1.8755626920562477e-255

1.4081474353677686e-251

2.9058779586404625e-253

-6.419132125800359e-131

-1.2340554909025647e-137

-1.2574376283715415e-137

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	85
1	62	85

end0.0ms

sample908.0ms

Algorithm

intervals

Results

289.0ms	6034×	body	80	valid
183.0ms	649×	body	2560	valid
116.0ms	486×	body	1280	valid
101.0ms	298×	body	5120	valid
51.0ms	285×	body	640	valid
22.0ms	166×	body	320	valid
7.0ms	82×	body	160	valid

Details

analyze335.0ms

sample34.0ms

simplify3.0ms

prune7.0ms

localize10.0ms

rewrite20.0ms

series38.0ms

simplify51.0ms

prune128.0ms

localize11.0ms

rewrite28.0ms

series52.0ms

simplify58.0ms

prune141.0ms

localize17.0ms

rewrite26.0ms

series103.0ms

simplify49.0ms

prune146.0ms

localize18.0ms

rewrite21.0ms

series92.0ms

simplify56.0ms

prune96.0ms

regimes348.0ms

bsearch49.0ms

simplify2.0ms

end0.0ms

sample908.0ms

Profiling