Details

sample46.0ms

Algorithm

intervals

Results

32.0ms

269×

body

valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.9b	(+ (* x.re y.re) (* x.im y.im))
29.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite51.0ms

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))
7.0ms	(+ (* x.re y.re) (* x.im y.im))
36.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series172.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* y.re y.re) (* y.im y.im))
42.0ms	(+ (* x.re y.re) (* x.im y.im))
102.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify894.0ms

Counts

65 → 65

Iterations

Iter	Nodes
done	2002
3	2002
2	1139
1	285
0	101

prune651.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 29.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
16.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite61.0ms

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))
33.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* x.re y.re) (* x.im y.im))
160.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
56.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify852.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	2007
3	2007
2	905
1	283
0	120

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 27.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.9b	(+ (* x.re y.re) (* x.im y.im))
1.1b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
29.0b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`times-frac` `add-cube-cbrt`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`div-exp` `prod-exp` `associate-/r/` `insert-posit16`
3×	`associate-/r` `associate-l` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 101

Calls

4 calls:

7.0ms	(+ (* y.re y.re) (* y.im y.im))
13.0ms	(+ (* x.re y.re) (* x.im y.im))
21.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
43.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series255.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (* y.re y.re) (* y.im y.im))
39.0ms	(+ (* x.re y.re) (* x.im y.im))
57.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
106.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify1.3s

Counts

113 → 113

Iterations

Iter	Nodes
done	2015
3	2015
2	1597
1	416
0	143

prune1.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 27.0b

localize48.0ms

Local error

Found 4 expressions with local error:

17.4b	(cbrt (+ (* x.re y.re) (* x.im y.im)))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`sqrt-div`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 62

Calls

4 calls:

4.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
67.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

74 → 74

Iterations

Iter	Nodes
done	2000
4	2000
3	1480
2	623
1	259
0	101

prune1.2s

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 27.0b

regimes338.0ms

Accuracy

0% (2.6b remaining)

Error of 25.8b against oracle of 23.2b and baseline of 25.8b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.0s

8488×

body

valid