Details

sample43.0ms

Algorithm

intervals

Results

21.0ms

267×

body

valid

simplify83.0ms

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize20.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
25.2b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite49.0ms

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:

8.0ms	(- (* x.im y.re) (* x.re y.im))
40.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series203.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(- (* x.im y.re) (* x.re y.im))
143.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify934.0ms

Counts

50 → 50

Iterations

Useful iterations: done (932.0ms)

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

prune198.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
16.2b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite72.0ms

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:

12.0ms	(- (* x.im y.re) (* x.re y.im))
38.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* x.im y.re) (* x.re y.im))
168.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
61.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify971.0ms

Counts

98 → 98

Iterations

Useful iterations: done (967.0ms)

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

prune439.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
0.8b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
24.6b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3-+` `1-exp` `associate-*l/` `cbrt-unprod` `flip-+` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 87

Calls

3 calls:

8.0ms	(- (* x.im y.re) (* x.re y.im))
28.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
92.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series246.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(- (* x.im y.re) (* x.re y.im))
62.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
130.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify3.3s

Counts

96 → 96

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	128	1631
1	365	1521
2	2532	1304
done	5000	1302

prune372.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.4b

localize28.0ms

Local error

Found 4 expressions with local error:

11.6b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

41.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series512.0ms

Counts

4 → 12

Calls

4 calls:

333.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
61.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
60.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.3s

Counts

113 → 113

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	144	2355
1	340	2146
2	1176	2035
3	4836	2006
done	5000	2006

prune506.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 21.4b

regimes147.0ms

Accuracy

0% (3.1b remaining)

Error of 25.9b against oracle of 22.8b and baseline of 25.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	25
1	16	25
done	16	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

757.0ms

8438×

body

valid