Details

sample20.0ms

Algorithm

intervals

Results

8.0ms

267×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7
done	15	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
23.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite44.0ms

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:

12.0ms	(+ (* y.re y.re) (* y.im y.im))
30.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series119.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(+ (* y.re y.re) (* y.im y.im))
88.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify112.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	241	453
1	1058	412
2	3964	410
3	5002	410
done	5002	410

prune127.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* 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))))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 264

Calls

4 calls:

259.0ms	(/ (/ (+ (* 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))))
30.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (/ (+ (* 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))))
109.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify80.0ms

Counts

276 → 276

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	714	5680
1	2516	5201
2	5001	5144
done	5001	5144

prune516.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.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))))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite137.0ms

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×	`flip3-+` `associate-/r*` `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` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 160

Calls

4 calls:

83.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
32.0ms	(/ (+ (* 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)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
110.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify78.0ms

Counts

172 → 172

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	567	2505
1	3282	2242
2	5001	2117
done	5001	2117

prune400.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 20.8b

localize14.0ms

Local error

Found 4 expressions with local error:

15.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

31.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify71.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	242	919
1	758	870
2	2276	857
3	5001	857
done	5001	857

prune288.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 20.8b

regimes202.0ms

Accuracy

19.5% (2.4b remaining)

Error of 24.7b against oracle of 22.3b and baseline of 25.2b

bsearch4.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	26
1	27	26
done	27	26

end0.0ms

sample570.0ms

Algorithm

intervals

Results

275.0ms

8463×

body

valid