Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	200×	body	80	valid
3.0ms	18×	body	2560	valid
2.0ms	10×	body	5120	valid
2.0ms	14×	body	1280	valid
1.0ms	6×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite62.0ms

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:

22.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
31.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series258.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
45.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

49 → 49

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	99	722
1	243	617
2	642	569
3	1604	542
4	4024	537
done	5000	537

prune145.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (sqrt (+ (* re re) (* im im))) re))
0.3b	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

34.0ms	(sqrt (+ (sqrt (+ (* re re) (* im im))) re))
80.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
31.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt (+ (sqrt (+ (* re re) (* im im))) re))
175.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts

88 → 88

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	143	1421
1	339	1237
2	936	1163
3	2332	1127
done	5000	1119

prune220.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
3.8b	(exp (log (* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

80.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
28.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
93.0ms	(exp (log (* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
8.0ms	(sqrt (+ (* re re) (* im im)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
51.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
168.0ms	(exp (log (* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

90 → 90

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	151	1490
1	327	1281
2	897	1204
3	2335	1162
done	5000	1154

prune271.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 15.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
3.8b	(pow E (log (* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`pow1` `*-un-lft-identity`
14×	`sqrt-prod`
11×	`add-cube-cbrt`
7×	`add-exp-log` `pow-unpow` `associate-r`
6×	`sqrt-div` `associate-l` `pow-prod-down` `add-cbrt-cube` `add-log-exp`
5×	`sqrt-pow1` `pow1/2`
4×	`flip3-+` `associate-*r/` `log-pow` `flip-+` `unswap-sqr`
3×	`unpow-prod-down`
2×	`log-div` `pow-exp` `distribute-lft-out` `pow-sub`
1×	`unpow-prod-up` `+-commutative` `pow-to-exp` `rem-sqrt-square` `e-exp-1` `log-prod` `pow-pow` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 85

Calls

4 calls:

80.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
27.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
37.0ms	(pow E (log (* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
8.0ms	(sqrt (+ (* re re) (* im im)))

series1.1s

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
829.0ms	(pow E (log (* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

97 → 97

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	174	1748
1	409	1538
2	1113	1453
3	2942	1408
done	5001	1396

prune274.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 15.4b

regimes307.0ms

Accuracy

58.3% (8.9b remaining)

Error of 26.0b against oracle of 17.1b and baseline of 38.4b

bsearch89.0ms

Steps

Iters	Range		Point
10	9.511609313434486e+66	1.6770313419776726e+82	2.23943936895026e+78
9	-1.8500422114427506e-302	-2.113572165822749e-307	-2.142078331456716e-307

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	52
1	37	52
done	37	52

end0.0ms

sample689.0ms

Algorithm

intervals

Results

194.0ms	6072×	body	80	valid
132.0ms	700×	body	2560	valid
75.0ms	507×	body	1280	valid
69.0ms	299×	body	5120	valid
27.0ms	232×	body	640	valid
11.0ms	123×	body	320	valid
4.0ms	67×	body	160	valid