Details

sample48.0ms

Algorithm

intervals

Results

33.0ms

274×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
25.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite62.0ms

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

Counts

3 → 56

Calls

3 calls:

7.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(+ (* x.re y.re) (* x.im y.im))
46.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series177.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* y.re y.re) (* y.im y.im))
45.0ms	(+ (* x.re y.re) (* x.im y.im))
100.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify515.0ms

Counts

65 → 65

Iterations

Iter	Nodes
done	2002
2	1139
1	285
0	101

prune318.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
15.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite76.0ms

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-+`
4×	`insert-posit16`
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 → 88

Calls

4 calls:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
43.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* x.re y.re) (* x.im y.im))
128.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
48.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
50.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify564.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	2000
2	905
1	283
0	120

prune536.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
15.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite54.0ms

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-+`
4×	`insert-posit16`
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 → 88

Calls

4 calls:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
30.0ms	(/ (+ (* 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)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (* x.re y.re) (* x.im y.im))
158.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
46.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
59.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify617.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	2000
2	905
1	283
0	120

prune559.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 23.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
0.7b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
24.6b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite78.0ms

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×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16`
2×	`+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `1-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 141

Calls

4 calls:

13.0ms	(+ (* y.re y.re) (* y.im y.im))
9.0ms	(+ (* x.re y.re) (* x.im y.im))
17.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
36.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (* y.re y.re) (* y.im y.im))
39.0ms	(+ (* x.re y.re) (* x.im y.im))
186.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
79.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify797.0ms

Counts

153 → 153

Iterations

Iter	Nodes
done	2001
2	1769
1	575
0	210

prune866.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 23.3b

regimes508.0ms

Accuracy

0% (1.7b remaining)

Error of 25.6b against oracle of 23.9b and baseline of 25.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.4s

8466×

body

valid