Details

sample35.0ms

Algorithm

intervals

Results

23.0ms

273×

body

valid

simplify57.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	70
5	70
4	66
3	48
2	36
1	19
0	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize30.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (* x.im y.re) (* x.re y.im))
27.5b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite41.0ms

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` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

2 → 46

Calls

2 calls:

8.0ms	(- (* x.im y.re) (* x.re y.im))
33.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series166.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(- (* x.im y.re) (* x.re y.im))
118.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

52 → 52

Iterations

Iter	Nodes
done	2001
3	2001
2	896
1	260
0	91

prune338.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 27.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* x.im y.re) (* x.re y.im))
16.2b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite50.0ms

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`
4×	`insert-posit16`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 90

Calls

4 calls:

14.0ms	(- (* x.im y.re) (* x.re y.im))
22.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* x.im y.re) (* x.re y.im))
159.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
62.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
63.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts

102 → 102

Iterations

Iter	Nodes
done	2000
3	2000
2	934
1	315
0	124

prune571.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 25.7b

localize40.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
0.6b	(- (* x.im y.re) (* x.re y.im))
27.5b	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
55×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`insert-posit16`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/l/`
1×	`sub-neg` `flip3-+` `diff-log` `flip-+` `pow-flip` `inv-pow`

Counts

3 → 130

Calls

3 calls:

27.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
11.0ms	(- (* x.im y.re) (* x.re y.im))
54.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

series347.0ms

Counts

3 → 9

Calls

3 calls:

205.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
61.0ms	(- (* x.im y.re) (* x.re y.im))
80.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

simplify1.4s

Counts

139 → 139

Iterations

Iter	Nodes
done	2000
3	2000
2	1455
1	530
0	198

prune912.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 25.7b

localize53.0ms

Local error

Found 4 expressions with local error:

16.2b	(/ (- (* x.im y.re) (* x.re y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

30×	`sqrt-div`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `flip3-+` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod` `flip-+`
8×	`associate-/r/`
7×	`pow1`
4×	`frac-times` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `times-frac` `pow1/2` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-r/` `associate-/l/`
1×	`clear-num` `associate-/r*` `frac-2neg` `flip3--` `div-sub` `prod-exp` `cbrt-unprod` `div-inv` `flip--`

Counts

4 → 81

Calls

4 calls:

66.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
70.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
62.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
69.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	2002
3	2002
2	836
1	304
0	112

prune669.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 25.7b

regimes568.0ms

Accuracy

0% (2.7b remaining)

Error of 25.8b against oracle of 23.1b and baseline of 25.8b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	15

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

8485×

body

valid