Details

sample46.0ms

Algorithm

intervals

Results

9.0ms	30×	body	2560	valid
9.0ms	185×	body	80	valid
5.0ms	18×	body	1280	valid
3.0ms	8×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	15
1	22	15
2	24	15
done	24	15

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.3b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
28.3b	(sqrt (+ (* re re) (* im im)))

rewrite90.0ms

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:

41.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
38.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series404.0ms

Counts

3 → 9

Calls

3 calls:

253.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
82.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
68.0ms	(sqrt (+ (* re re) (* im im)))

simplify733.0ms

Counts

49 → 49

Iterations

Useful iterations: done (731.0ms)

Iter	Nodes	Cost
0	99	722
1	251	621
2	954	569
done	5001	545

prune309.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.1b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
28.3b	(sqrt (+ (* re re) (* im im)))
28.3b	(sqrt (+ (* re re) (* im im)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
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×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

80.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
53.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))
11.0ms	(sqrt (+ (* re re) (* im im)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
88.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
63.0ms	(sqrt (+ (* re re) (* im im)))
58.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

136 → 136

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	133	3041
1	300	1750
2	1110	1579
done	5000	1544

prune620.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
28.3b	(sqrt (+ (* re re) (* im im)))
29.0b	(sqrt (* 2.0 (+ (* im im) 0)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt` `sqrt-prod`
37×	`*-un-lft-identity`
36×	`times-frac`
25×	`add-cube-cbrt`
12×	`difference-of-squares`
9×	`associate-/r*`
8×	`pow1` `sqrt-div`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp`
4×	`associate-r/` `associate-/l`
3×	`sqrt-pow1` `flip3-+` `flip-+`
2×	`flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `clear-num` `div-inv`

Counts

4 → 109

Calls

4 calls:

82.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
58.0ms	(- (sqrt (+ (* re re) (* im im))) re)
18.0ms	(sqrt (+ (* re re) (* im im)))
21.0ms	(sqrt (* 2.0 (+ (* im im) 0)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
76.0ms	(- (sqrt (+ (* re re) (* im im))) re)
68.0ms	(sqrt (+ (* re re) (* im im)))
60.0ms	(sqrt (* 2.0 (+ (* im im) 0)))

simplify1.4s

Counts

121 → 121

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	212	2952
1	473	2509
2	2240	2366
done	5000	2346

prune734.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (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)
28.3b	(sqrt (+ (* re re) (* im im)))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
61×	`sqrt-prod`
58×	`times-frac`
57×	`*-un-lft-identity`
41×	`add-cube-cbrt`
33×	`associate-r`
16×	`difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*`
8×	`distribute-lft-out--`
7×	`pow1`
6×	`sqrt-div` `associate-l` `add-log-exp` `unswap-sqr`
4×	`associate-/r/`
3×	`flip3--` `flip--` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip-+`

Counts

4 → 142

Calls

4 calls:

46.0ms	(/ (fabs im) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
147.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
71.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ (fabs im) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
238.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
66.0ms	(- (sqrt (+ (* re re) (* im im))) re)
67.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.2s

Counts

154 → 154

Iterations

Useful iterations: 2 (768.0ms)

Iter	Nodes	Cost
0	271	3346
1	696	3072
2	4590	2896
done	5000	2896

prune831.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.8b

regimes406.0ms

Accuracy

54.5% (13.2b remaining)

Error of 21.0b against oracle of 7.8b and baseline of 36.8b

bsearch254.0ms

Steps

Iters	Range		Point
8	1.421260319246115e-59	2.2979305419496232e-55	9.422701723781502e-57
5	1.1787098984122044e-83	4.1597825206829345e-83	1.7001244109494596e-83
6	1.1467790892721152e-96	5.188403161073841e-96	5.1251846534840524e-96
5	-2.822584078228535e+117	-1.0610906721978556e+117	-2.4740957117892876e+117

simplify14.0ms

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	41	99
1	55	92
done	55	92

end0.0ms

sample2.1s

Algorithm

intervals

Results

609.0ms	308×	body	5120	valid
591.0ms	6022×	body	80	valid
251.0ms	671×	body	2560	valid
181.0ms	472×	body	1280	valid
72.0ms	300×	body	640	valid
27.0ms	149×	body	320	valid
10.0ms	78×	body	160	valid