Details

sample44.0ms

Algorithm

intervals

Results

31.0ms

274×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	15
1	15
0	11

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize29.0ms

Local error

Found 2 expressions with local error:

0.9b	(+ (* 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)))

rewrite60.0ms

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

Counts

2 → 44

Calls

2 calls:

15.0ms	(+ (* x.re y.re) (* x.im y.im))
38.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series173.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(+ (* x.re y.re) (* x.im y.im))
132.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify904.0ms

Counts

50 → 50

Iterations

Iter	Nodes
3	2585
2	802
1	238
0	88

prune558.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
16.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.1b	(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:

13.0ms	(+ (* x.re y.re) (* x.im y.im))
37.0ms	(/ (+ (* 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)))
18.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* x.re y.re) (* x.im y.im))
135.0ms	(/ (+ (* 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)))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify845.0ms

Counts

100 → 100

Iterations

Iter	Nodes
3	2632
2	899
1	282
0	120

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 23.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
16.5b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp` `insert-posit16`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 98

Calls

4 calls:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
48.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* x.re y.re) (* x.im y.im))
148.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify3.3s

Counts

110 → 110

Iterations

Iter	Nodes
3	3845
2	1190
1	400
0	149

prune1.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 23.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.5b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
0.9b	(+ (* x.re y.re) (* x.im y.im))
24.8b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 89

Calls

3 calls:

11.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(+ (* x.re y.re) (* x.im y.im))
66.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series241.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
51.0ms	(+ (* x.re y.re) (* x.im y.im))
121.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify5.1s

Counts

98 → 98

Iterations

Iter	Nodes
3	4246
2	1376
1	370
0	130

prune999.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 23.4b

regimes477.0ms

Accuracy

0% (2.4b remaining)

Error of 26.0b against oracle of 23.5b and baseline of 26.0b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	20
1	20
0	15

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.2s

8475×

body

valid