Details

sample54.0ms

Algorithm

intervals

Results

23.0ms

267×

body

valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize31.0ms

Local error

Found 2 expressions with local error:

0.2b	(+ (* x.re y.re) (* x.im y.im))
25.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite82.0ms

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:

14.0ms	(+ (* x.re y.re) (* x.im y.im))
65.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series181.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(+ (* x.re y.re) (* x.im y.im))
136.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify915.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (141.0ms)

Iter	Nodes	Cost
0	86	924
1	238	906
2	1009	824
done	5000	824

prune314.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 25.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* x.re y.re) (* x.im y.im))
13.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite91.0ms

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:

20.0ms	(+ (* x.re y.re) (* x.im y.im))
49.0ms	(/ (+ (* 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:

55.0ms	(+ (* x.re y.re) (* x.im y.im))
158.0ms	(/ (+ (* 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)))
70.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify951.0ms

Counts

96 → 96

Iterations

Useful iterations: done (947.0ms)

Iter	Nodes	Cost
0	117	1780
1	280	1649
2	1173	1543
done	5000	1541

prune945.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* y.im x.im) (* y.re x.re))
13.5b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* y.re x.re)))
30.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite73.0ms

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:

10.0ms	(+ (* y.im x.im) (* y.re x.re))
37.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* y.re x.re)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (* y.im x.im) (* y.re x.re))
134.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* y.re x.re)))
42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts

96 → 96

Iterations

Useful iterations: 3 (587.0ms)

Iter	Nodes	Cost
0	113	1774
1	268	1656
2	839	1556
3	2843	1540
done	5001	1540

prune610.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* x.re y.re) (* x.im y.im))
13.6b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
30.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite133.0ms

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:

14.0ms	(+ (* x.re y.re) (* x.im y.im))
80.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
18.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* x.re y.re) (* x.im y.im))
181.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
44.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify3.4s

Counts

106 → 106

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	146	1886
1	408	1701
2	2341	1478
done	5002	1474

prune627.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 23.3b

regimes472.0ms

Accuracy

0% (2.9b remaining)

Error of 25.9b against oracle of 22.9b and baseline of 25.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	27
1	21	27
done	21	27

end0.0ms

sample1.2s

Algorithm

intervals

Results

688.0ms

8517×

body

valid