Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	198×	body	80	valid
3.0ms	18×	body	2560	valid
3.0ms	17×	body	1280	valid
2.0ms	11×	body	5120	valid
1.0ms	5×	body	640	valid
0.0ms	5×	body	160	valid
0.0ms	2×	body	320	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	8
done	33	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.4b	(+ (sqrt (+ (* re re) (* im im))) re)
30.3b	(sqrt (+ (* re re) (* im im)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
7×	`pow1` `add-sqr-sqrt` `sqrt-prod`
6×	`add-cube-cbrt` `fma-def`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `pow-prod-down` `sum-log` `hypot-def` `distribute-lft-out`

Counts

3 → 53

Calls

3 calls:

23.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
34.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series257.0ms

Counts

3 → 9

Calls

3 calls:

172.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify76.0ms

Counts

62 → 62

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	264	372
1	830	337
2	2660	322
3	5002	320
done	5002	320

prune175.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 6.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
1.4b	(+ re (hypot re im))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
6×	`*-un-lft-identity`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt` `associate-*r/`
3×	`add-exp-log` `expm1-log1p-u` `fma-def` `sqrt-pow1` `pow-prod-down` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`+-commutative` `hypot-udef` `pow1/2` `sum-log` `sqrt-prod` `distribute-lft-out`

Counts

3 → 43

Calls

3 calls:

0.0ms	(hypot re im)
22.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
5.0ms	(+ re (hypot re im))

series291.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(hypot re im)
184.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
58.0ms	(+ re (hypot re im))

simplify84.0ms

Counts

52 → 52

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	208	209
1	808	191
2	3269	185
3	5001	185
done	5001	185

prune145.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ re (hypot re im)))
0.0b	(hypot re im)
0.4b	(* (sqrt 2.0) (sqrt (+ re (hypot re im))))
1.4b	(+ re (hypot re im))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`sqrt-prod`
10×	`add-cube-cbrt`
9×	`pow1`
7×	`associate-r`
6×	`add-exp-log` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out`
2×	`associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `hypot-udef` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

4 → 81

Calls

4 calls:

7.0ms	(sqrt (+ re (hypot re im)))
0.0ms	(hypot re im)
26.0ms	(* (sqrt 2.0) (sqrt (+ re (hypot re im))))
5.0ms	(+ re (hypot re im))

series413.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(sqrt (+ re (hypot re im)))
45.0ms	(hypot re im)
184.0ms	(* (sqrt 2.0) (sqrt (+ re (hypot re im))))
60.0ms	(+ re (hypot re im))

simplify114.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	301	456
1	1012	426
2	4364	411
3	5001	411
done	5001	411

prune235.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im)))))
0.3b	(* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im))))
1.4b	(+ re (hypot re im))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

31×	`sqrt-prod`
25×	`add-sqr-sqrt`
18×	`associate-l`
17×	`*-un-lft-identity`
16×	`pow1`
13×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow-prod-down`
8×	`associate-r`
6×	`associate-*r/` `add-log-exp` `unswap-sqr`
5×	`sqrt-pow1` `pow1/2`
4×	`expm1-log1p-u` `sqrt-div` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `sqrt-unprod` `flip-+`
2×	`*-commutative` `distribute-lft-out`
1×	`+-commutative` `hypot-udef` `sum-log`

Counts

4 → 98

Calls

4 calls:

0.0ms	(hypot re im)
50.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im)))))
28.0ms	(* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im))))
6.0ms	(+ re (hypot re im))

series532.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot re im)
188.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im)))))
239.0ms	(* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im))))
59.0ms	(+ re (hypot re im))

simplify45.0ms

Counts

110 → 110

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	361	743
1	1458	666
2	5002	653
done	5002	653

prune280.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

regimes78.0ms

Accuracy

30.7% (4.1b remaining)

Error of 11.4b against oracle of 7.3b and baseline of 13.2b

bsearch41.0ms

Steps

Iters	Range		Point
7	-7.339202252346793e+19	-8.375797978149412e+17	-5.229117268898384e+18

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	12
1	28	12
done	28	12

end0.0ms

sample695.0ms

Algorithm

intervals

Results

193.0ms	6042×	body	80	valid
139.0ms	718×	body	2560	valid
68.0ms	293×	body	5120	valid
66.0ms	451×	body	1280	valid
32.0ms	276×	body	640	valid
12.0ms	138×	body	320	valid
5.0ms	82×	body	160	valid