Details

sample37.0ms

Algorithm

intervals

Results

16.0ms

277×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize16.0ms

Local error

Found 2 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
24.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite61.0ms

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/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 42

Calls

2 calls:

6.0ms	(+ (* x.re y.re) (* x.im y.im))
54.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series204.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(+ (* x.re y.re) (* x.im y.im))
143.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.2s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
3	4323
2	906
1	237
0	86

prune326.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 24.3b

localize29.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
16.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite66.0ms

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-+`
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 → 84

Calls

4 calls:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
35.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* 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))))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1173
1	280
0	117

prune566.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.7b

localize32.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
1.2b	(+ (* x.re y.re) (* x.im y.im))
24.4b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 126

Calls

3 calls:

34.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
12.0ms	(+ (* x.re y.re) (* x.im y.im))
31.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series321.0ms

Counts

3 → 9

Calls

3 calls:

176.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
40.0ms	(+ (* x.re y.re) (* x.im y.im))
104.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify2.2s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
2	3600
1	539
0	194

prune908.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 21.7b

localize32.0ms

Local error

Found 3 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
1.2b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
23.8b	(* (/ 1 (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))

rewrite79.0ms

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-l`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`flip3-+` `flip-+` `add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-/r` `associate-r` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*r/` `cbrt-unprod` `div-inv`
1×	`distribute-rgt-in` `+-commutative` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `-commutative` `pow-flip` `inv-pow`

Counts

3 → 87

Calls

3 calls:

6.0ms	(+ (* x.re y.re) (* x.im y.im))
18.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
50.0ms	(* (/ 1 (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))

series277.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (* x.re y.re) (* x.im y.im))
46.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
190.0ms	(* (/ 1 (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))

simplify2.6s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	4206
1	502
0	135

prune501.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 21.7b

regimes509.0ms

Accuracy

54.8% (1.0b remaining)

Error of 24.7b against oracle of 23.7b and baseline of 25.9b

bsearch2.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	31
1	31
0	22

end0.0ms

sample1.1s

Algorithm

intervals

Results

739.0ms

8465×

body

valid