Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	180×	body	80	valid
4.0ms	24×	body	2560	valid
4.0ms	18×	body	5120	valid
3.0ms	17×	body	1280	valid
1.0ms	11×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	8
1	28	8
2	36	8
3	44	8
4	46	8
5	46	8
done	46	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
17×	`sqrt-prod`
7×	`pow1`
6×	`fma-neg`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `pow-prod-down` `flip-+` `hypot-def` `distribute-lft-out--`

Counts

3 → 74

Calls

3 calls:

51.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series268.0ms

Counts

3 → 9

Calls

3 calls:

178.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
51.0ms	(- (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify42.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	314	760
1	1192	522
2	5001	473
done	5001	473

prune187.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
0.0b	(hypot re im)
0.7b	(- (* 1 (hypot re im)) re)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 44

Calls

3 calls:

19.0ms	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
0.0ms	(hypot re im)
8.0ms	(- (* 1 (hypot re im)) re)

series302.0ms

Counts

3 → 9

Calls

3 calls:

190.0ms	(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))
51.0ms	(hypot re im)
61.0ms	(- (* 1 (hypot re im)) re)

simplify32.0ms

Counts

53 → 53

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	235	265
1	803	220
2	5002	213
done	5002	213

prune146.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.6b	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
14×	`*-un-lft-identity`
13×	`add-cube-cbrt`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`prod-diff` `pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

0.0ms	(hypot re im)
2.0ms	(hypot re im)
12.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
29.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

series211.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot re im)
48.0ms	(hypot re im)
51.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
61.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

simplify41.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	211	391
1	869	298
2	5001	281
done	5001	281

prune235.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.6b	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)
8.6b	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)
8.6b	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`pow1`
18×	`*-un-lft-identity` `sqrt-prod`
15×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`prod-diff`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `pow-sqr` `flip--` `distribute-lft-out--`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 108

Calls

4 calls:

12.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
31.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)
29.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)
32.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

series237.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
63.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)
60.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)
64.0ms	(- (* 1 (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

simplify48.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	201	697
1	856	482
2	5001	445
done	5001	445

prune344.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.2b

regimes96.0ms

Accuracy

31.8% (3.9b remaining)

Error of 11.3b against oracle of 7.4b and baseline of 13.1b

bsearch60.0ms

Steps

Iters	Range		Point
11	3.802331011621998e-21	5.276955647516397	4.717568369814921e-15

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	37	14
2	37	14
done	37	14

end0.0ms

sample704.0ms

Algorithm

intervals

Results

194.0ms	6004×	body	80	valid
128.0ms	688×	body	2560	valid
80.0ms	320×	body	5120	valid
75.0ms	492×	body	1280	valid
32.0ms	250×	body	640	valid
14.0ms	161×	body	320	valid
5.0ms	85×	body	160	valid