Details

sample32.0ms

Algorithm

intervals

Results

22.0ms

264×

body

valid

simplify38.0ms

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(- (* x.im y.re) (* x.re y.im))
28.8b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 58

Calls

3 calls:

14.0ms	(+ (* y.re y.re) (* y.im y.im))
20.0ms	(- (* x.im y.re) (* x.re y.im))
20.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series227.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(+ (* y.re y.re) (* y.im y.im))
45.0ms	(- (* x.im y.re) (* x.re y.im))
137.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify969.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
2	1790
1	320
0	104

prune376.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 28.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
18.9b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite65.0ms

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:

10.0ms	(- (* x.im y.re) (* x.re y.im))
36.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* x.im y.re) (* x.re y.im))
161.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1193
1	315
0	124

prune618.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.8b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.im y.im) (* y.re y.re))
0.2b	(- (* x.im y.re) (* x.re y.im))
28.8b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.im y.im) (* y.re y.re)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 58

Calls

3 calls:

13.0ms	(+ (* y.im y.im) (* y.re y.re))
12.0ms	(- (* x.im y.re) (* x.re y.im))
42.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.im y.im) (* y.re y.re)))

series172.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* y.im y.im) (* y.re y.re))
44.0ms	(- (* x.im y.re) (* x.re y.im))
97.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.im y.im) (* y.re y.re)))

simplify951.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
2	1687
1	314
0	104

prune339.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.8b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.im y.im) (* y.re y.re))
0.2b	(- (* x.im y.re) (* x.re y.im))
0.3b	(/ 1 (/ (+ (* y.im y.im) (* y.re y.re)) (- (* x.im y.re) (* x.re y.im))))
28.7b	(/ (+ (* y.im y.im) (* y.re y.re)) (- (* x.im y.re) (* x.re y.im)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`div-exp` `add-log-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 142

Calls

4 calls:

7.0ms	(+ (* y.im y.im) (* y.re y.re))
16.0ms	(- (* x.im y.re) (* x.re y.im))
34.0ms	(/ 1 (/ (+ (* y.im y.im) (* y.re y.re)) (- (* x.im y.re) (* x.re y.im))))
51.0ms	(/ (+ (* y.im y.im) (* y.re y.re)) (- (* x.im y.re) (* x.re y.im)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* y.im y.im) (* y.re y.re))
44.0ms	(- (* x.im y.re) (* x.re y.im))
212.0ms	(/ 1 (/ (+ (* y.im y.im) (* y.re y.re)) (- (* x.im y.re) (* x.re y.im))))
81.0ms	(/ (+ (* y.im y.im) (* y.re y.re)) (- (* x.im y.re) (* x.re y.im)))

simplify1.8s

Counts

154 → 154

Iterations

Iter	Nodes
done	5000
2	3829
1	592
0	211

prune654.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.8b

regimes384.0ms

Accuracy

-9.7% (3.0b remaining)

Error of 26.2b against oracle of 23.2b and baseline of 25.9b

bsearch111.0ms

Steps

Iters	Range		Point
4	2.99988769581893e+36	5.314606313626179e+36	5.2422713568197025e+36
9	-3.137566432904386e+97	-7.171553699074835e+91	-1.2109434524169916e+96

simplify6.0ms

Iterations

Iter	Nodes
done	26
1	26
0	22

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

8412×

body

valid