Details

sample282.0ms

Algorithm

intervals

Results

210.0ms

263×

body

valid

simplify37.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize43.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
25.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 42

Calls

2 calls:

151.0ms	(+ (* x.re y.re) (* x.im y.im))
66.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series805.0ms

Counts

2 → 6

Calls

2 calls:

214.0ms	(+ (* x.re y.re) (* x.im y.im))
589.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify5.7s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
3	2808
2	856
1	238
0	86

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.8b

localize76.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
16.1b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `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` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

40.0ms	(+ (* x.re y.re) (* x.im y.im))
160.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (* x.re y.re) (* x.im y.im))
326.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
76.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
91.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify6.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
3	2674
2	906
1	280
0	117

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.4b

localize64.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
16.2b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `add-cbrt-cube` `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` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

16.0ms	(+ (* x.re y.re) (* x.im y.im))
48.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(+ (* x.re y.re) (* x.im y.im))
160.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
73.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
72.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify5.2s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
3	2260
2	797
1	270
0	115

prune2.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.4b

localize126.0ms

Local error

Found 3 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
1.2b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
24.3b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 126

Calls

3 calls:

17.0ms	(+ (* x.re y.re) (* x.im y.im))
50.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
133.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series477.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(+ (* x.re y.re) (* x.im y.im))
296.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
114.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify4.9s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
2	1524
1	532
0	194

prune2.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 22.4b

regimes2.6s

Accuracy

0% (2.9b remaining)

Error of 25.9b against oracle of 23.0b and baseline of 25.9b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample8.5s

Algorithm

intervals

Results

7.9s

8479×

body

valid