Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

268×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(+ (* x.re y.re) (* x.im y.im))
27.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

6.0ms	(+ (* y.re y.re) (* y.im y.im))
6.0ms	(+ (* x.re y.re) (* x.im y.im))
23.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series162.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
37.0ms	(+ (* x.re y.re) (* x.im y.im))
94.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.0s

Counts

62 → 62

Iterations

Iter	Nodes
done	5005
3	4355
2	1069
1	281
0	98

prune332.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 27.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* 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))))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

6.0ms	(+ (* x.re y.re) (* x.im y.im))
30.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* x.re y.re) (* x.im y.im))
142.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.9s

Counts

96 → 96

Iterations

Iter	Nodes
done	5002
3	2699
2	906
1	280
0	117

prune567.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.8b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
17.2b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

14.0ms	(+ (* x.re y.re) (* x.im y.im))
29.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (* x.re y.re) (* x.im y.im))
128.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.9s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
3	2261
2	797
1	270
0	115

prune633.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(+ (* x.re y.re) (* x.im y.im))
0.6b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
27.2b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

11.0ms	(+ (* y.re y.re) (* y.im y.im))
11.0ms	(+ (* x.re y.re) (* x.im y.im))
43.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
45.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* y.re y.re) (* y.im y.im))
48.0ms	(+ (* x.re y.re) (* x.im y.im))
187.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
101.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify1.6s

Counts

149 → 149

Iterations

Iter	Nodes
done	5002
2	1848
1	570
0	206

prune846.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 23.8b

regimes410.0ms

Accuracy

0% (3.0b remaining)

Error of 26.7b against oracle of 23.6b and baseline of 26.7b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample1.3s

Algorithm

intervals

Results

965.0ms

8480×

body

valid