Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
3.0ms	18×	body	2560	valid
3.0ms	17×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	6×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	15
1	22	15
2	23	15
done	23	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
27.4b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

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:

11.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series262.0ms

Counts

3 → 9

Calls

3 calls:

178.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify840.0ms

Counts

49 → 49

Iterations

Useful iterations: done (839.0ms)

Iter	Nodes	Cost
0	99	722
1	243	617
2	667	569
3	1886	542
done	5001	541

prune175.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.4b	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
27.4b	(sqrt (+ (* re re) (* im im)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`sqrt-prod`
12×	`*-un-lft-identity`
8×	`pow1` `add-cube-cbrt`
7×	`associate-r`
6×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`associate-*r/` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

3 → 60

Calls

3 calls:

42.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series260.0ms

Counts

3 → 9

Calls

3 calls:

176.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

69 → 69

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	122	1096
1	290	967
2	861	908
3	2693	883
done	5001	882

prune196.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 16.4b

localize14.0ms

Local error

Found 4 expressions with local error:

12.0b	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
27.4b	(sqrt (+ (* re re) (* im im)))
27.4b	(sqrt (+ (* re re) (* im im)))
27.4b	(sqrt (+ (* re re) (* im im)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log`

Counts

4 → 56

Calls

4 calls:

38.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

68 → 68

Iterations

Useful iterations: 4 (585.0ms)

Iter	Nodes	Cost
0	62	1223
1	162	1127
2	399	661
3	1164	622
4	3721	614
done	5000	614

prune273.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (* 2.0 (+ 0 (* im im)))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.9b	(- (sqrt (+ (* re re) (* im im))) re)
26.4b	(sqrt (* 2.0 (+ 0 (* im im))))
27.4b	(sqrt (+ (* re re) (* im im)))

rewrite53.0ms

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:

25.0ms	(/ (sqrt (* 2.0 (+ 0 (* im im)))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
18.0ms	(- (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (* 2.0 (+ 0 (* im im))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (sqrt (* 2.0 (+ 0 (* im im)))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (* 2.0 (+ 0 (* im im))))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts

121 → 121

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	212	2952
1	441	2510
2	1291	2370
3	4774	2333
done	5000	2333

prune345.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.3b

regimes210.0ms

Accuracy

55.7% (12.0b remaining)

Error of 22.1b against oracle of 10.2b and baseline of 37.2b

bsearch105.0ms

Steps

Iters	Range		Point
7	5.023487767188019e-90	3.713870109526283e-88	9.989819735270073e-90
10	-2.7283838574175814e+156	-2.4047927607493394e+144	-1.3292486390963865e+154

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	35	51
1	44	49
done	44	49

end0.0ms

sample655.0ms

Algorithm

intervals

Results

188.0ms	6020×	body	80	valid
141.0ms	719×	body	2560	valid
75.0ms	479×	body	1280	valid
65.0ms	266×	body	5120	valid
33.0ms	280×	body	640	valid
15.0ms	163×	body	320	valid
5.0ms	73×	body	160	valid