Details

sample53.0ms

Algorithm

intervals

Results

31.0ms

271×

body

valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 26.6b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.1b	(+ (* x.re y.re) (* x.im y.im))
26.1b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

12.0ms	(+ (* y.re y.re) (* y.im y.im))
20.0ms	(+ (* x.re y.re) (* x.im y.im))
60.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series203.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (* y.re y.re) (* y.im y.im))
37.0ms	(+ (* x.re y.re) (* x.im y.im))
121.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts

62 → 62

Iterations

Useful iterations: 2 (169.0ms)

Iter	Nodes	Cost
0	99	1090
1	270	1067
2	866	951
3	2515	951
done	5001	951

prune306.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.8b

localize29.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (* x.re y.re) (* x.im y.im))
17.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite79.0ms

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:

16.0ms	(+ (* x.re y.re) (* x.im y.im))
42.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (* x.re y.re) (* x.im y.im))
176.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts

96 → 96

Iterations

Useful iterations: 3 (665.0ms)

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

prune401.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (* x.re y.re) (* x.im y.im))
17.3b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite111.0ms

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` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
74.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (* x.re y.re) (* x.im y.im))
176.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
56.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.5s

Counts

106 → 106

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	146	1886
1	378	1642
2	1154	1474
3	3751	1458
done	5001	1458

prune627.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 22.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.im y.im) (* y.re y.re))
1.1b	(+ (* x.re y.re) (* x.im y.im))
26.1b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.im y.im) (* y.re y.re)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

19.0ms	(+ (* y.im y.im) (* y.re y.re))
13.0ms	(+ (* x.re y.re) (* x.im y.im))
54.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.im y.im) (* y.re y.re)))

series236.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(+ (* y.im y.im) (* y.re y.re))
58.0ms	(+ (* x.re y.re) (* x.im y.im))
133.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.im y.im) (* y.re y.re)))

simplify1.8s

Counts

62 → 62

Iterations

Useful iterations: 2 (183.0ms)

Iter	Nodes	Cost
0	99	1090
1	270	1067
2	866	951
3	2516	951
done	5001	951

prune204.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 22.2b

regimes190.0ms

Accuracy

3.8% (2.9b remaining)

Error of 26.0b against oracle of 23.1b and baseline of 26.1b

bsearch64.0ms

Steps

Iters	Range		Point
9	1.820441680002137e+102	5.1868391204133894e+107	7.389276722766794e+104

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample1.2s

Algorithm

intervals

Results

831.0ms

8514×

body

valid