Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

271×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	15	15
done	15	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.8b	(+ (* x.re y.re) (* x.im y.im))
27.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite15.0ms

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:

2.0ms	(+ (* x.re y.re) (* x.im y.im))
11.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series113.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+ (* x.re y.re) (* x.im y.im))
78.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

48 → 48

Iterations

Useful iterations: 3 (341.0ms)

Iter	Nodes	Cost
0	86	924
1	231	906
2	718	824
3	2140	820
done	5000	820

prune149.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 27.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* x.re y.re) (* x.im y.im))
14.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

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:

2.0ms	(+ (* x.re y.re) (* x.im y.im))
12.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* x.re y.re) (* x.im y.im))
110.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts

96 → 96

Iterations

Useful iterations: 3 (365.0ms)

Iter	Nodes	Cost
0	117	1780
1	274	1649
2	751	1541
3	2033	1525
done	5001	1525

prune299.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 26.5b

localize19.0ms

Local error

Found 4 expressions with local error:

14.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`sqrt-prod`
18×	`times-frac`
8×	`sqrt-div`
7×	`pow1`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 88

Calls

4 calls:

12.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.3s

Counts

100 → 100

Iterations

Useful iterations: 3 (305.0ms)

Iter	Nodes	Cost
0	105	1833
1	244	1680
2	643	1570
3	1695	1548
4	4883	1548
done	5000	1548

prune349.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 26.5b

localize18.0ms

Local error

Found 4 expressions with local error:

10.7b	(/ (+ (* x.im y.im) (* x.re y.re)) (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))))
33.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.8b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
34.8b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`cbrt-div` `flip3-+` `flip-+` `add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`pow1/3` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 70

Calls

4 calls:

8.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
2.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
2.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
93.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
96.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts

82 → 82

Iterations

Useful iterations: 3 (456.0ms)

Iter	Nodes	Cost
0	140	1569
1	307	1499
2	884	1341
3	2748	1335
done	5001	1335

prune353.0ms

Pruning

13 alts after pruning (9 fresh and 4 done)

Merged error: 26.5b

regimes266.0ms

Accuracy

11% (2.7b remaining)

Error of 26.4b against oracle of 23.7b and baseline of 26.7b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	64
1	24	64
done	24	64

end0.0ms

sample512.0ms

Algorithm

intervals

Results

294.0ms

8497×

body

valid