Details

sample38.0ms

Algorithm

intervals

Results

17.0ms

267×

body

valid

simplify73.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	19	15
2	36	15
3	48	15
4	66	15
5	72	15
done	72	15

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
27.6b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite60.0ms

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×	`associate-/r` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

17.0ms	(- (* x.im y.re) (* x.re y.im))
41.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series161.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(- (* x.im y.re) (* x.re y.im))
116.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify772.0ms

Counts

50 → 50

Iterations

Useful iterations: done (770.0ms)

Iter	Nodes	Cost
0	89	954
1	259	936
2	1133	856
done	5001	854

prune319.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 27.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
18.0b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite101.0ms

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`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

19.0ms	(- (* x.im y.re) (* x.re y.im))
50.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* x.im y.re) (* x.re y.im))
143.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify912.0ms

Counts

98 → 98

Iterations

Useful iterations: done (908.0ms)

Iter	Nodes	Cost
0	121	1814
1	313	1682
2	1219	1576
done	5000	1574

prune610.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.2b

localize31.0ms

Local error

Found 4 expressions with local error:

18.0b	(/ (- (* x.im y.re) (* x.re y.im)) (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.0b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
31.0b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

32.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series757.0ms

Counts

4 → 12

Calls

4 calls:

471.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
50.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
130.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
106.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts

79 → 79

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	160	1768
1	446	1671
2	2139	1433
done	5000	1427

prune716.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 25.2b

localize40.0ms

Local error

Found 4 expressions with local error:

7.8b	(cbrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
27.6b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
27.6b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
27.6b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

18.0ms	(cbrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
37.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
48.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
42.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series703.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(cbrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
133.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
127.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
144.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts

132 → 132

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	155	3148
1	383	3093
2	1455	2842
done	5001	2826

prune783.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 25.2b

regimes578.0ms

Accuracy

20.5% (2.3b remaining)

Error of 25.2b against oracle of 22.9b and baseline of 25.8b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	53
1	21	53
done	21	53

end0.0ms

sample1.1s

Algorithm

intervals

Results

628.0ms

8517×

body

valid