Details

sample37.0ms

Algorithm

intervals

Results

17.0ms

271×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	284
1	15	284
done	15	284

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize33.0ms

Local error

Found 2 expressions with local error:

0.2b	(+ (* x.re y.re) (* x.im y.im))
22.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite69.0ms

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

Counts

2 → 42

Calls

2 calls:

6.0ms	(+ (* x.re y.re) (* x.im y.im))
62.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series194.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(+ (* x.re y.re) (* x.im y.im))
146.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.7s

Counts

48 → 48

Iterations

Useful iterations: 2 (189.0ms)

Iter	Nodes	Cost
0	86	16901
1	237	16036
2	906	15956
3	4323	15956
done	5001	15956

prune340.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* x.re y.re) (* x.im y.im))
14.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite49.0ms

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:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
26.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* x.re y.re) (* x.im y.im))
121.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts

96 → 96

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	117	34504
1	280	32109
2	1173	32109
done	5001	32069

prune508.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 19.6b

localize35.0ms

Local error

Found 4 expressions with local error:

14.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

30×	`sqrt-div`
12×	`add-sqr-sqrt`
10×	`flip3-+` `flip-+`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod`
8×	`associate-/r/`
7×	`pow1`
4×	`frac-times` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `times-frac` `pow1/2` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-r/` `associate-/l/`
1×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

43.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
43.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.0s

Counts

88 → 88

Iterations

Useful iterations: 2 (215.0ms)

Iter	Nodes	Cost
0	107	30665
1	279	25870
2	812	25790
3	2619	25790
done	5000	25790

prune651.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 19.6b

localize38.0ms

Local error

Found 4 expressions with local error:

14.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (cbrt (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.re y.re) (* y.im y.im)))))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.8b	(cbrt (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.re y.re) (* y.im y.im))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

33.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (cbrt (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* 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)))
22.0ms	(cbrt (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.re y.re) (* y.im y.im))))

series279.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (cbrt (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.re y.re) (* y.im y.im)))))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
53.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
47.0ms	(cbrt (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.re y.re) (* y.im y.im))))

simplify1.4s

Counts

101 → 101

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	144	46458
1	348	42087
2	1122	42007
done	5000	37207

prune632.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 19.6b

regimes547.0ms

Accuracy

0% (3.1b remaining)

Error of 26.7b against oracle of 23.6b and baseline of 26.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	364
1	17	364
done	17	364

end0.0ms

sample1.3s

Algorithm

intervals

Results

969.0ms

8463×

body

valid