Details

sample60.0ms

Algorithm

intervals

Results

41.0ms

272×

body

valid

simplify87.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.0b	(- (* x.im y.re) (* x.re y.im))
25.8b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite60.0ms

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

Counts

3 → 58

Calls

3 calls:

7.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(- (* x.im y.re) (* x.re y.im))
43.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series224.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (* y.re y.re) (* y.im y.im))
47.0ms	(- (* x.im y.re) (* x.re y.im))
128.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify941.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	2001
3	2001
2	1186
1	305
0	104

prune628.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
17.0b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite116.0ms

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

Counts

4 → 270

Calls

4 calls:

51.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
166.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
59.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts

282 → 282

Iterations

Iter	Nodes
done	2000
2	2000
1	745
0	310

prune3.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.7b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.0b	(- (* x.im y.re) (* x.re y.im))
25.8b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite52.0ms

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

Counts

3 → 58

Calls

3 calls:

7.0ms	(+ (* y.re y.re) (* y.im y.im))
9.0ms	(- (* x.im y.re) (* x.re y.im))
35.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series234.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(+ (* y.re y.re) (* y.im y.im))
53.0ms	(- (* x.im y.re) (* x.re y.im))
137.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify964.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	2001
3	2001
2	1186
1	305
0	104

prune751.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 23.7b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
17.0b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite148.0ms

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*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `insert-posit16` `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` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 165

Calls

4 calls:

83.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
30.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
20.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
170.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts

177 → 177

Iterations

Iter	Nodes
done	2005
3	2005
2	1840
1	596
0	199

prune2.4s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 23.7b

regimes601.0ms

Accuracy

0% (2.6b remaining)

Error of 25.6b against oracle of 23.0b and baseline of 25.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.5s

8470×

body

valid