Details

sample56.0ms

Algorithm

intervals

Results

40.0ms

270×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	15
1	15
0	11

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize43.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x.re y.re) (* x.im y.im))
28.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite59.0ms

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

Counts

2 → 44

Calls

2 calls:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
51.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series164.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(+ (* x.re y.re) (* x.im y.im))
112.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify755.0ms

Counts

50 → 50

Iterations

Iter	Nodes
3	2585
2	802
1	238
0	88

prune540.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 27.8b

localize56.0ms

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))))
18.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite172.0ms

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

Counts

4 → 268

Calls

4 calls:

85.0ms	(/ (/ (+ (* 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))))
54.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (/ (+ (* 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))))
176.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
62.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.8s

Counts

280 → 280

Iterations

Iter	Nodes
3	6045
2	1718
1	721
0	305

prune2.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 25.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
18.7b	(/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite154.0ms

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*` `flip3-+` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
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` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 164

Calls

4 calls:

78.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
58.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (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)))

series498.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
148.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
66.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
63.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify7.5s

Counts

176 → 176

Iterations

Iter	Nodes
3	7458
2	1941
1	594
0	196

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.im y.im) (* x.re y.re))))
18.8b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.im y.im) (* x.re y.re)))
33.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
100×	`add-sqr-sqrt`
98×	`*-un-lft-identity` `add-cube-cbrt`
54×	`sqrt-prod`
27×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
9×	`associate-/l*`
8×	`flip3-+` `div-exp` `flip-+`
7×	`pow1`
6×	`sqrt-div` `div-inv`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 197

Calls

4 calls:

20.0ms	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.im y.im) (* x.re y.re))))
25.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.im y.im) (* x.re y.re)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.im y.im) (* x.re y.re))))
86.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.im y.im) (* x.re y.re)))
46.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
44.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify5.9s

Counts

209 → 209

Iterations

Iter	Nodes
3	4745
2	1574
1	633
0	245

prune2.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 24.4b

regimes413.0ms

Accuracy

0% (3.4b remaining)

Error of 26.2b against oracle of 22.8b and baseline of 26.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	15
1	15
0	11

end0.0ms

sample1.4s

Algorithm

intervals

Results

987.0ms

8484×

body

valid