Details

sample31.0ms

Algorithm

intervals

Results

21.0ms

269×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	15
1	15
0	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize29.0ms

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)))

rewrite54.0ms

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:

12.0ms	(+ (* y.re y.re) (* y.im y.im))
12.0ms	(+ (* x.re y.re) (* x.im y.im))
29.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series194.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* y.re y.re) (* y.im y.im))
41.0ms	(+ (* x.re y.re) (* x.im y.im))
125.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.4s

Counts

65 → 65

Iterations

Iter	Nodes
3	4222
2	1140
1	284
0	101

prune746.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 29.4b

localize25.0ms

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)))

rewrite62.0ms

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))
38.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* x.re y.re) (* x.im y.im))
124.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
50.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
53.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify779.0ms

Counts

100 → 100

Iterations

Iter	Nodes
3	2632
2	899
1	282
0	120

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 27.0b

localize28.0ms

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))))

rewrite71.0ms

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))
10.0ms	(+ (* x.re y.re) (* x.im y.im))
16.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series236.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* y.re y.re) (* y.im y.im))
47.0ms	(+ (* x.re y.re) (* x.im y.im))
50.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
94.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify4.7s

Counts

113 → 113

Iterations

Iter	Nodes
3	6008
2	1606
1	413
0	143

prune1.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 27.0b

localize66.0ms

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)))

rewrite29.0ms

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:

7.0ms	(cbrt (+ (* x.re y.re) (* x.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)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts

74 → 74

Iterations

Iter	Nodes
4	3900
3	1449
2	612
1	258
0	101

prune1.2s

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 27.0b

regimes437.0ms

Accuracy

0% (2.6b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	17
1	17
0	13

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.7s

8488×

body

valid