Details

sample82.0ms

Algorithm

intervals

Results

28.0ms	190×	body	80	valid
17.0ms	25×	body	2560	valid
10.0ms	12×	body	5120	valid
9.0ms	15×	body	1280	valid
4.0ms	8×	body	640	valid
2.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	24
2	24
1	22
0	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize21.0ms

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)
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite71.0ms

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:

25.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
24.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
21.0ms	(sqrt (+ (* re re) (* im im)))

series356.0ms

Counts

3 → 9

Calls

3 calls:

236.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
76.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
45.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.0s

Counts

52 → 52

Iterations

Iter	Nodes
done	2001
3	2001
2	669
1	246
0	102

prune579.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
1.3b	(- (sqrt (+ (* re re) (* im im))) re)
27.3b	(sqrt (* 2.0 (+ (* im im) 0)))
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite115.0ms

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:

51.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
35.0ms	(- (sqrt (+ (* re re) (* im im))) re)
15.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
12.0ms	(sqrt (+ (* re re) (* im im)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
59.0ms	(- (sqrt (+ (* re re) (* im im))) re)
47.0ms	(sqrt (* 2.0 (+ (* im im) 0)))
49.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts

125 → 125

Iterations

Iter	Nodes
done	2000
3	2000
2	1114
1	452
0	216

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.3b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.4b	(* (sqrt 2.0) (fabs im))
1.3b	(- (sqrt (+ (* re re) (* im im))) re)
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite98.0ms

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 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
10.0ms	(* (sqrt 2.0) (fabs im))
36.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
47.0ms	(* (sqrt 2.0) (fabs im))
72.0ms	(- (sqrt (+ (* re re) (* im im))) re)
46.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.2s

Counts

103 → 103

Iterations

Iter	Nodes
done	2011
3	2011
2	1538
1	463
0	194

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (fabs im))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (fabs im)))
1.3b	(- (sqrt (+ (* re re) (* im im))) re)
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

61.0ms	(/ (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (fabs im))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (fabs im)))
63.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(/ (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (fabs im))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
41.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (fabs im)))
67.0ms	(- (sqrt (+ (* re re) (* im im))) re)
49.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

107 → 107

Iterations

Iter	Nodes
done	2092
3	2092
2	1808
1	521
0	203

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.3b

regimes691.0ms

Accuracy

69.1% (9.0b remaining)

Error of 16.5b against oracle of 7.4b and baseline of 36.6b

bsearch393.0ms

Steps

Iters	Range	Point
9	4.7599761429228367e+98	9.416899659600005e+104	9.299865300702547e+104
9	-2.3066181393648038e-248	-3.0719470799760817e-257	-3.1198242249434154e-257
10	-5.119440634421198e+122	-1.7867168956050676e+111	-3.2601941440528353e+122

Iters

Range

Point

4.7599761429228367e+98

9.416899659600005e+104

9.299865300702547e+104

-2.3066181393648038e-248

-3.0719470799760817e-257

-3.1198242249434154e-257

-5.119440634421198e+122

-1.7867168956050676e+111

-3.2601941440528353e+122

simplify15.0ms

Iterations

Iter	Nodes
done	57
1	57
0	42

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	5970×	body	80	valid
491.0ms	703×	body	2560	valid
361.0ms	481×	body	1280	valid
279.0ms	307×	body	5120	valid
128.0ms	289×	body	640	valid
85.0ms	167×	body	320	valid
17.0ms	83×	body	160	valid