Details

sample61.0ms

Algorithm

intervals

Results

16.0ms	191×	body	80	valid
9.0ms	14×	body	2560	valid
8.0ms	13×	body	5120	valid
8.0ms	18×	body	1280	valid
4.0ms	14×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	24
2	24
1	22
0	12

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
31.5b	(sqrt (+ (* re re) (* im im)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-log-exp`
4×	`sqrt-div` `add-cube-cbrt` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `pow-prod-down` `distribute-lft-out`

Counts

3 → 43

Calls

3 calls:

29.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
21.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

series353.0ms

Counts

3 → 9

Calls

3 calls:

220.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
69.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
64.0ms	(sqrt (+ (* re re) (* im im)))

simplify619.0ms

Counts

52 → 52

Iterations

Iter	Nodes
done	2001
2	669
1	246
0	102

prune371.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.4b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (+ (* re re) (* im im))) re)
0.2b	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
30.2b	(sqrt (* 2.0 (+ (* im im) 0)))
31.5b	(sqrt (+ (* re re) (* im im)))

rewrite124.0ms

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-cbrt-cube` `add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`associate-r/` `insert-posit16` `associate-/l`
3×	`sqrt-pow1` `flip3-+` `flip-+`
2×	`flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `div-inv`

Counts

4 → 113

Calls

4 calls:

58.0ms	(- (sqrt (+ (* re re) (* im im))) re)
50.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (sqrt (+ (* re re) (* im im))) re)
243.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
38.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
61.0ms	(sqrt (+ (* re re) (* im im)))

simplify863.0ms

Counts

125 → 125

Iterations

Iter	Nodes
done	2001
2	1123
1	452
0	216

prune650.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.4b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (+ (* re re) (* im im))) re)
0.2b	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.4b	(* (sqrt 2.0) (fabs im))
31.5b	(sqrt (+ (* re re) (* im im)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`sqrt-prod`
18×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `times-frac`
7×	`pow1`
6×	`associate-l` `add-log-exp` `difference-of-squares`
4×	`sqrt-div` `insert-posit16`
3×	`associate-r` `distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

4 → 91

Calls

4 calls:

43.0ms	(- (sqrt (+ (* re re) (* im im))) re)
36.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(* (sqrt 2.0) (fabs im))
6.0ms	(sqrt (+ (* re re) (* im im)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (sqrt (+ (* re re) (* im im))) re)
200.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
45.0ms	(* (sqrt 2.0) (fabs im))
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify820.0ms

Counts

103 → 103

Iterations

Iter	Nodes
done	2041
2	1546
1	463
0	194

prune609.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (+ (* re re) (* im im))) re)
0.3b	(/ (fabs im) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.4b	(* (sqrt 2.0) (/ (fabs im) (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
31.5b	(sqrt (+ (* re re) (* im im)))

rewrite241.0ms

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-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
8×	`distribute-lft-out--`
7×	`pow1`
6×	`sqrt-div` `associate-l` `add-log-exp` `unswap-sqr`
4×	`associate-/r/` `insert-posit16`
3×	`flip3--` `flip--` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `associate-r/` `-commutative` `flip-+`

Counts

4 → 146

Calls

4 calls:

59.0ms	(- (sqrt (+ (* re re) (* im im))) re)
40.0ms	(/ (fabs im) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
129.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
6.0ms	(sqrt (+ (* re re) (* im im)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (sqrt (+ (* re re) (* im im))) re)
139.0ms	(/ (fabs im) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
197.0ms	(* (sqrt 2.0) (/ (fabs im) (sqrt (- (sqrt (+ (* re re) (* im im))) re))))
60.0ms	(sqrt (+ (* re re) (* im im)))

simplify646.0ms

Counts

158 → 158

Iterations

Iter	Nodes
done	2000
1	669
0	267

prune852.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.5b

regimes599.0ms

Accuracy

66% (9.9b remaining)

Error of 17.5b against oracle of 7.6b and baseline of 36.9b

bsearch396.0ms

Steps

Iters	Range		Point
8	1.1138250880895117e+95	3.6742441519344763e+99	9.701163352497263e+98
10	2.6703922475793124e-253	7.076344427023373e-242	2.4935750622148784e-246
6	-6.493281180427814e-218	-1.272279862751547e-218	-3.263660527236801e-218
11	-1.4727407547297607e+132	-9.242862080727889e+95	-1.1214463413730795e+123

simplify13.0ms

Iterations

Iter	Nodes
done	62
1	62
0	47

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	5988×	body	80	valid
604.0ms	695×	body	2560	valid
289.0ms	296×	body	5120	valid
273.0ms	481×	body	1280	valid
169.0ms	302×	body	640	valid
53.0ms	158×	body	320	valid
16.0ms	80×	body	160	valid