Details

sample30.0ms

Algorithm

intervals

Results

13.0ms

265×

body

valid

simplify4.0ms

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: 24.6b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x.re y.re) (* x.im y.im))
24.1b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
35.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series159.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(+ (* x.re y.re) (* x.im y.im))
108.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.0s

Counts

48 → 48

Iterations

Useful iterations: 3 (865.0ms)

Iter	Nodes	Cost
0	86	924
1	237	906
2	906	824
3	4323	820
done	5001	820

prune333.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
15.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`*-un-lft-identity` `add-cube-cbrt`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*` `flip3-+` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 264

Calls

4 calls:

61.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
157.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts

276 → 276

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	302	11076
1	755	9987
2	3738	9426
done	5000	9054

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
15.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*` `flip3-+` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative`

Counts

4 → 161

Calls

4 calls:

113.0ms	(* (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
56.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
152.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
43.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify4.7s

Counts

173 → 173

Iterations

Useful iterations: done (4.7s)

Iter	Nodes	Cost
0	196	4846
1	608	4527
2	3837	4052
done	5000	4038

prune842.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.8b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x.re y.re) (* x.im y.im))
0.6b	(/ (/ 1 1) (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
23.7b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

474×	`times-frac`
221×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
38×	`add-exp-log`
32×	`div-inv`
31×	`associate-/r/`
30×	`div-exp`
18×	`associate-/r*`
17×	`flip3-+` `add-cbrt-cube` `flip-+`
16×	`associate-/l*`
10×	`1-exp`
9×	`cbrt-undiv`
5×	`add-log-exp`
4×	`rec-exp`
3×	`pow1` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log`

Counts

3 → 295

Calls

3 calls:

11.0ms	(+ (* x.re y.re) (* x.im y.im))
32.0ms	(/ (/ 1 1) (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
41.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series335.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(+ (* x.re y.re) (* x.im y.im))
194.0ms	(/ (/ 1 1) (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
79.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify1.3s

Counts

304 → 304

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	481	11053
1	1818	9038
done	5000	8745

prune702.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 20.8b

regimes473.0ms

Accuracy

3.7% (2.7b remaining)

Error of 25.7b against oracle of 23.0b and baseline of 25.8b

bsearch46.0ms

Steps

Iters	Range		Point
8	2.586892949274192e+85	1.392645936715808e+88	1.2655629246867158e+88

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.1s

Algorithm

intervals

Results

701.0ms

8448×

body

valid