Details

sample44.0ms

Algorithm

intervals

Results

22.0ms

275×

body

valid

simplify58.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	70
5	70
4	66
3	48
2	36
1	19
0	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize27.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
24.4b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite51.0ms

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` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

11.0ms	(- (* x.im y.re) (* x.re y.im))
38.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series195.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- (* x.im y.re) (* x.re y.im))
145.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify3.1s

Counts

50 → 50

Iterations

Iter	Nodes
done	5000
3	3011
2	887
1	258
0	89

prune389.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 24.2b

localize46.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
15.4b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite81.0ms

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`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 86

Calls

4 calls:

11.0ms	(- (* x.im y.re) (* x.re y.im))
41.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (* x.im y.re) (* x.re y.im))
178.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.3s

Counts

98 → 98

Iterations

Iter	Nodes
done	5005
3	2678
2	935
1	313
0	121

prune742.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.4b

localize29.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
1.1b	(- (* x.im y.re) (* x.re y.im))
24.3b	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

rewrite102.0ms

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

Counts

3 → 127

Calls

3 calls:

40.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
11.0ms	(- (* x.im y.re) (* x.re y.im))
43.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

series341.0ms

Counts

3 → 9

Calls

3 calls:

197.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
63.0ms	(- (* x.im y.re) (* x.re y.im))
81.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

simplify1.8s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	1529
1	533
0	195

prune843.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.4b

localize38.0ms

Local error

Found 4 expressions with local error:

15.4b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.3b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
32.3b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
6×	`cbrt-prod` `associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`cbrt-div` `flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`associate-/l*`
2×	`pow1/3` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-sub` `div-exp` `div-inv` `flip--`

Counts

4 → 85

Calls

4 calls:

34.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
144.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
174.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	2846
2	899
1	327
0	135

prune706.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 22.4b

regimes488.0ms

Accuracy

0% (3.1b remaining)

Error of 25.9b against oracle of 22.8b and baseline of 25.9b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample972.0ms

Algorithm

intervals

Results

665.0ms

8432×

body

valid