Details

sample43.0ms

Algorithm

intervals

Results

29.0ms

273×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize47.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
24.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite48.0ms

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

Counts

3 → 56

Calls

3 calls:

7.0ms	(+ (* y.re y.re) (* y.im y.im))
7.0ms	(+ (* x.re y.re) (* x.im y.im))
34.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series189.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (* y.re y.re) (* y.im y.im))
48.0ms	(+ (* x.re y.re) (* x.im y.im))
99.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify754.0ms

Counts

65 → 65

Iterations

Iter	Nodes
done	2002
3	2002
2	1139
1	285
0	101

prune398.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
13.1b	(/ (+ (* 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)))

rewrite78.0ms

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-+`
4×	`insert-posit16`
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 → 88

Calls

4 calls:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
45.0ms	(/ (+ (* 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)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* x.re y.re) (* x.im y.im))
138.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
60.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
56.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify895.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	2007
3	2007
2	905
1	283
0	120

prune609.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
0.5b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
24.1b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`times-frac` `add-cube-cbrt`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`div-exp` `prod-exp` `associate-/r/` `insert-posit16`
3×	`associate-/r` `associate-l` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 101

Calls

4 calls:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
14.0ms	(+ (* x.re y.re) (* x.im y.im))
16.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
40.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series241.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* y.re y.re) (* y.im y.im))
39.0ms	(+ (* x.re y.re) (* x.im y.im))
55.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
107.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify799.0ms

Counts

113 → 113

Iterations

Iter	Nodes
done	2015
3	2015
2	1597
1	416
0	143

prune524.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
24.1b	(* (+ (* x.re y.re) (* x.im y.im)) (/ (/ 1 (sqrt (+ (* y.re y.re) (* y.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

270×	`times-frac`
173×	`add-sqr-sqrt`
150×	`associate-r`
141×	`sqrt-prod`
138×	`*-un-lft-identity`
134×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`sqrt-div`
14×	`associate-/r/`
13×	`add-cbrt-cube`
12×	`flip3-+` `flip-+` `unswap-sqr`
8×	`pow1` `div-inv`
6×	`div-exp` `add-log-exp`
5×	`prod-exp`
4×	`insert-posit16`
3×	`cbrt-undiv` `associate-l` `cbrt-unprod`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/`
1×	`+-commutative` `rec-exp` `sum-log` `1-exp` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 232

Calls

4 calls:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
59.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* x.re y.re) (* x.im y.im))
96.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
46.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

244 → 244

Iterations

Iter	Nodes
done	2000
2	2000
1	1050
0	348

prune912.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.5b

regimes398.0ms

Accuracy

0% (2.6b remaining)

Error of 25.5b against oracle of 22.9b and baseline of 25.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.6s

8496×

body

valid