Details

sample43.0ms

Algorithm

intervals

Results

16.0ms

276×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	15	15
done	15	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize19.0ms

Local error

Found 2 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
29.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

19.0ms	(+ (* x.re y.re) (* x.im y.im))
38.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series156.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(+ (* x.re y.re) (* x.im y.im))
97.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts

48 → 48

Iterations

Useful iterations: 3 (629.0ms)

Iter	Nodes	Cost
0	86	924
1	232	906
2	767	824
3	2337	820
done	5000	820

prune201.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 29.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* 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))))
32.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `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` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

15.0ms	(+ (* x.re y.re) (* x.im y.im))
68.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* x.re y.re) (* x.im y.im))
141.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.6s

Counts

96 → 96

Iterations

Useful iterations: 3 (558.0ms)

Iter	Nodes	Cost
0	117	1780
1	275	1649
2	775	1541
3	2060	1525
done	5000	1525

prune400.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 26.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
17.6b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
32.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

12.0ms	(+ (* x.re y.re) (* x.im y.im))
25.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (* x.re y.re) (* x.im y.im))
97.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
62.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify4.4s

Counts

96 → 96

Iterations

Useful iterations: 3 (569.0ms)

Iter	Nodes	Cost
0	115	1774
1	265	1656
2	723	1554
3	1742	1540
4	4598	1540
done	5001	1540

prune472.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 26.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.8b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
0.9b	(+ (* x.re y.re) (* x.im y.im))
28.5b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 126

Calls

3 calls:

26.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
16.0ms	(+ (* x.re y.re) (* x.im y.im))
65.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series330.0ms

Counts

3 → 9

Calls

3 calls:

203.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
35.0ms	(+ (* x.re y.re) (* x.im y.im))
91.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify2.9s

Counts

135 → 135

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	194	3510
1	468	3261
2	1271	2982
3	4125	2954
done	5000	2954

prune376.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 26.0b

regimes280.0ms

Accuracy

3% (2.9b remaining)

Error of 26.6b against oracle of 23.7b and baseline of 26.7b

bsearch53.0ms

Steps

Iters	Range		Point
8	2.5603685361688665e+88	1.193256888551369e+92	1.0220962851570888e+92

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	39
1	21	39
done	21	39

end0.0ms

sample781.0ms

Algorithm

intervals

Results

374.0ms

8487×

body

valid