Details

sample34.0ms

Algorithm

intervals

Results

19.0ms

273×

body

valid

simplify45.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	70
5	70
4	66
3	48
2	36
1	19
0	11

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize25.0ms

Local error

Found 2 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
24.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite34.0ms

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` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

2 → 46

Calls

2 calls:

8.0ms	(- (* x.im y.re) (* x.re y.im))
25.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series168.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- (* x.im y.re) (* x.re y.im))
117.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.5s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
3	3031
2	896
1	260
0	91

prune329.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
15.0b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite86.0ms

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`
4×	`insert-posit16`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 90

Calls

4 calls:

8.0ms	(- (* 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))))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* x.im y.re) (* x.re y.im))
172.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
58.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
53.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5006
3	2657
2	934
1	315
0	124

prune622.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 21.6b

localize58.0ms

Local error

Found 4 expressions with local error:

29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
19.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
66.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
69.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
43.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.8s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
5	3254
4	995
3	435
2	196
1	92
0	39

prune577.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 21.6b

localize54.0ms

Local error

Found 4 expressions with local error:

10.3b	(sqrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
10.3b	(sqrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
24.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
24.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
34×	`*-un-lft-identity` `add-cube-cbrt`
30×	`sqrt-prod`
8×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
6×	`pow1` `associate-/r` `associate-/l`
4×	`rem-sqrt-square` `flip3-+` `flip-+` `insert-posit16` `div-inv` `add-log-exp` `associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `div-exp` `flip--`

Counts

4 → 122

Calls

4 calls:

17.0ms	(sqrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
31.0ms	(sqrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
35.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series623.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(sqrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
169.0ms	(sqrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
160.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
141.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.6s

Counts

134 → 134

Iterations

Iter	Nodes
done	5012
3	2684
2	824
1	284
0	118

prune769.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 21.6b

regimes494.0ms

Accuracy

-0.3% (2.6b remaining)

Error of 25.6b against oracle of 23.0b and baseline of 25.6b

bsearch67.0ms

Steps

Iters	Range		Point
9	1.36934023547096e+82	3.0707098332476226e+88	7.672387965946081e+87

simplify5.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

8506×

body

valid