Details

sample39.0ms

Algorithm

intervals

Results

11.0ms	197×	body	80	valid
8.0ms	27×	body	2560	valid
3.0ms	9×	body	5120	valid
3.0ms	12×	body	1280	valid
2.0ms	9×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	15
1	17	15
2	24	15
3	29	15
4	33	15
done	33	15

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 37.2b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(- (sqrt (+ (* re re) (* im im))) re)
0.5b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

8.0ms	(- (sqrt (+ (* re re) (* im im))) re)
9.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series42.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(- (sqrt (+ (* re re) (* im im))) re)
26.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(sqrt (+ (* re re) (* im im)))

simplify650.0ms

Counts

52 → 52

Iterations

Useful iterations: 3 (215.0ms)

Iter	Nodes	Cost
0	104	782
1	231	687
2	799	635
3	2469	612
done	5000	612

prune109.0ms

Filtered

42 candidates to 52 candidates (-23.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	7	53

Merged error: 18.3b

Counts

53 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
0.7b	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
29.8b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (* 2.0 (+ (* im im) 0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
32×	`sqrt-prod`
28×	`times-frac`
24×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
8×	`pow1` `sqrt-div`
7×	`associate-/r*`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-r/` `associate-/l`
3×	`sqrt-pow1`
2×	`pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `clear-num` `sum-log` `div-inv`

Counts

4 → 96

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
16.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (* 2.0 (+ (* im im) 0)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
29.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (* 2.0 (+ (* im im) 0)))

simplify421.0ms

Counts

108 → 108

Iterations

Useful iterations: done (417.0ms)

Iter	Nodes	Cost
0	193	2513
1	441	2126
2	1390	1973
done	5000	1945

prune185.0ms

Filtered

81 candidates to 108 candidates (-33.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	106	9	115

Merged error: 11.0b

Counts

115 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
46×	`times-frac`
39×	`sqrt-prod`
37×	`add-cube-cbrt`
27×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out`
7×	`pow1` `associate-/r*`
6×	`sqrt-div` `associate-l` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r/` `flip-+`
3×	`associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 125

Calls

4 calls:

11.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
19.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
36.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
8.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify541.0ms

Counts

137 → 137

Iterations

Useful iterations: done (536.0ms)

Iter	Nodes	Cost
0	229	2936
1	563	2690
2	2281	2502
done	5000	2490

prune194.0ms

Filtered

89 candidates to 137 candidates (-53.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	137	9	146

Merged error: 8.1b

Counts

146 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) (fabs im))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
0.7b	(* (* (sqrt 2.0) (fabs im)) (/ 1 (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

30×	`-un-lft-identity` `associate-r*`
28×	`add-exp-log`
27×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
21×	`times-frac`
19×	`sqrt-prod`
18×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1`
7×	`associate-l` `cbrt-unprod`
6×	`add-log-exp`
4×	`sqrt-div` `div-exp` `pow-prod-down` `distribute-lft-out`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `sum-log` `un-div-inv` `div-inv`

Counts

4 → 101

Calls

4 calls:

5.0ms	(* (sqrt 2.0) (fabs im))
8.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
22.0ms	(* (* (sqrt 2.0) (fabs im)) (/ 1 (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt 2.0) (fabs im))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
29.0ms	(* (* (sqrt 2.0) (fabs im)) (/ 1 (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify629.0ms

Counts

113 → 113

Iterations

Useful iterations: done (626.0ms)

Iter	Nodes	Cost
0	211	1968
1	587	1712
2	2446	1465
done	5000	1438

prune139.0ms

Filtered

71 candidates to 113 candidates (-59.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	113	9	122

Merged error: 8.1b

Counts

122 → 9

regimes598.0ms

Accuracy

68.1% (9.7b remaining)

Error of 17.6b against oracle of 7.9b and baseline of 38.3b

bsearch101.0ms

Steps

Iters	Range		Point
9	3.43401543638109e+114	5.025550553073085e+120	4.40956572394349e+116
10	1.3994626587696508e-214	2.9831774035161146e-199	1.4225422339265396e-214
6	-3.9639939611996993e-296	-2.6703687768748694e-297	-7.88936342124095e-297
8	-1.0891331514545633e+114	-3.5827156305380124e+111	-4.6910854621363227e+113

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	83
1	61	83
done	61	83

end0.0ms

sample1.1s

Algorithm

intervals

Results

344.0ms	6084×	body	80	valid
219.0ms	687×	body	2560	valid
112.0ms	427×	body	1280	valid
108.0ms	291×	body	5120	valid
58.0ms	287×	body	640	valid
24.0ms	158×	body	320	valid
7.0ms	66×	body	160	valid

Details

sample39.0ms

simplify13.0ms

prune7.0ms

localize11.0ms

rewrite23.0ms

series42.0ms

simplify650.0ms

prune109.0ms

localize15.0ms

rewrite37.0ms

series47.0ms

simplify421.0ms

prune185.0ms

localize18.0ms

rewrite48.0ms

series72.0ms

simplify541.0ms

prune194.0ms

localize16.0ms

rewrite44.0ms

series53.0ms

simplify629.0ms

prune139.0ms

regimes598.0ms

bsearch101.0ms

simplify4.0ms

end0.0ms

sample1.1s

Profiling