Details

sample28.0ms

Algorithm

intervals

Results

12.0ms

263×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(+ (* x.re y.re) (* x.im y.im))
28.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite40.0ms

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))
27.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series611.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(+ (* y.re y.re) (* y.im y.im))
57.0ms	(+ (* x.re y.re) (* x.im y.im))
503.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify844.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
2	1625
1	296
0	98

prune424.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 28.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.im y.im) (* y.re x.re))
18.0b	(/ (+ (* x.im y.im) (* y.re x.re)) (sqrt (+ (* y.re y.re) (pow y.im 2))))
30.7b	(sqrt (+ (* y.re y.re) (pow y.im 2)))
30.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite89.0ms

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.im y.im) (* y.re x.re))
43.0ms	(/ (+ (* x.im y.im) (* y.re x.re)) (sqrt (+ (* y.re y.re) (pow y.im 2))))
14.0ms	(sqrt (+ (* y.re y.re) (pow y.im 2)))
23.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (* x.im y.im) (* y.re x.re))
195.0ms	(/ (+ (* x.im y.im) (* y.re x.re)) (sqrt (+ (* y.re y.re) (pow y.im 2))))
45.0ms	(sqrt (+ (* y.re y.re) (pow y.im 2)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify720.0ms

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1239
1	334
0	142

prune626.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 25.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
18.1b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
30.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite58.0ms

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:

12.0ms	(+ (* 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)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* x.re y.re) (* x.im y.im))
132.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.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)))

simplify2.2s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
3	4276
2	979
1	270
0	115

prune616.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 25.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.im y.im) (* y.re x.re))
18.1b	(* (+ (* x.im y.im) (* y.re x.re)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
30.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

6.0ms	(+ (* x.im y.im) (* y.re x.re))
65.0ms	(* (+ (* x.im y.im) (* y.re x.re)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* x.im y.im) (* y.re x.re))
194.0ms	(* (+ (* x.im y.im) (* y.re x.re)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
48.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify3.1s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	2313
1	408
0	145

prune668.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 25.2b

regimes572.0ms

Accuracy

35.1% (2.0b remaining)

Error of 25.4b against oracle of 23.4b and baseline of 26.4b

bsearch3.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	30
1	30
0	24

end0.0ms

sample1.3s

Algorithm

intervals

Results

732.0ms

8502×

body

valid