Details

sample44.0ms

Algorithm

intervals

Results

21.0ms

272×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
30.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 53

Calls

3 calls:

6.0ms	(+ (* y.re y.re) (* y.im y.im))
6.0ms	(+ (* x.re y.re) (* x.im y.im))
52.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series177.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* y.re y.re) (* y.im y.im))
38.0ms	(+ (* x.re y.re) (* x.im y.im))
103.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify983.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
2	1625
1	296
0	98

prune462.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 30.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
17.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 84

Calls

4 calls:

12.0ms	(+ (* x.re y.re) (* x.im y.im))
31.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ (* x.re y.re) (* x.im y.im))
157.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
68.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1173
1	280
0	117

prune610.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 27.9b

localize64.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
17.6b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
33.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

11.0ms	(+ (* x.re y.re) (* x.im y.im))
60.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* x.re y.re) (* x.im y.im))
183.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
68.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
69.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify3.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	2312
1	408
0	146

prune712.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 27.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
0.8b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
30.6b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `1-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

6.0ms	(+ (* y.re y.re) (* y.im y.im))
6.0ms	(+ (* x.re y.re) (* x.im y.im))
32.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
34.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* y.re y.re) (* y.im y.im))
42.0ms	(+ (* x.re y.re) (* x.im y.im))
208.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
100.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify2.1s

Counts

149 → 149

Iterations

Iter	Nodes
done	5001
2	4055
1	591
0	206

prune834.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 27.9b

regimes489.0ms

Accuracy

-20.3% (3.7b remaining)

Error of 27.2b against oracle of 23.5b and baseline of 26.6b

bsearch84.0ms

Steps

Iters	Range		Point
9	5.222295143107465e+216	6.592671542107617e+224	6.4954804305817955e+224

simplify3.0ms

Iterations

Iter	Nodes
done	24
1	24
0	18

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.2s

8471×

body

valid