Details

sample30.0ms

Algorithm

intervals

Results

6.0ms	186×	body	80	valid
4.0ms	22×	body	2560	valid
3.0ms	19×	body	1280	valid
3.0ms	11×	body	5120	valid
1.0ms	6×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8
done	35	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.5b	(- (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite74.0ms

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:

25.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
40.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

series255.0ms

Counts

3 → 9

Calls

3 calls:

169.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify73.0ms

Counts

52 → 52

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	232	382
1	768	356
2	2506	346
3	5001	344
done	5001	344

prune146.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.7b

localize13.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (+ (* re re) (* im im))) re)
1.5b	(- (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

38.0ms	(- (sqrt (+ (* re re) (* im im))) re)
40.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
50.0ms	(- (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify81.0ms

Counts

72 → 72

Iterations

Useful iterations: 4 (76.0ms)

Iter	Nodes	Cost
0	135	456
1	332	432
2	839	424
3	2503	422
4	5002	420
done	5002	420

prune223.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
10.0b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 126

Calls

4 calls:

52.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
39.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
48.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Counts

138 → 138

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	261	1112
1	935	975
2	5001	951
done	5001	951

prune287.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.7b

localize18.0ms

Local error

Found 4 expressions with local error:

29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

8.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify138.0ms

Counts

72 → 72

Iterations

Useful iterations: 5 (133.0ms)

Iter	Nodes	Cost
0	89	400
1	215	388
2	503	388
3	1265	388
4	4227	388
5	5002	384
done	5002	384

prune300.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 17.7b

regimes260.0ms

Accuracy

55.9% (9.1b remaining)

Error of 27.0b against oracle of 17.9b and baseline of 38.5b

bsearch111.0ms

Steps

Iters	Range	Point
10	7.495911143049393e-219	4.3617670924590225e-206	2.268707743098186e-218
8	2.604130790303375e-303	6.94733584068207e-301	4.2978556523375774e-301
7	-2.3797206039891623e+120	-3.6336066115999543e+118	-1.617907908010069e+120

Iters

Range

Point

7.495911143049393e-219

4.3617670924590225e-206

2.268707743098186e-218

2.604130790303375e-303

6.94733584068207e-301

4.2978556523375774e-301

-2.3797206039891623e+120

-3.6336066115999543e+118

-1.617907908010069e+120

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	35
1	55	35
2	55	35
done	55	35

end0.0ms

sample724.0ms

Algorithm

intervals

Results

197.0ms	5982×	body	80	valid
137.0ms	731×	body	2560	valid
87.0ms	518×	body	1280	valid
62.0ms	274×	body	5120	valid
35.0ms	270×	body	640	valid
13.0ms	149×	body	320	valid
5.0ms	76×	body	160	valid