Details

sample46.0ms

Algorithm

intervals

Results

22.0ms

271×

body

valid

simplify68.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	72
5	72
4	66
3	48
2	36
1	19
0	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize50.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
30.9b	(/ (- (* x.im y.re) (* x.re 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`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 55

Calls

3 calls:

6.0ms	(+ (* y.re y.re) (* y.im y.im))
6.0ms	(- (* x.im y.re) (* x.re y.im))
40.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series255.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* y.re y.re) (* y.im y.im))
71.0ms	(- (* x.im y.re) (* x.re y.im))
151.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
2	1834
1	319
0	101

prune513.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 30.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
17.6b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite55.0ms

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:

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

series289.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* x.im y.re) (* x.re y.im))
141.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1227
1	313
0	121

prune683.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 28.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
0.7b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
30.2b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite96.0ms

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`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-/r` `flip3-+` `flip3--` `associate-l` `flip-+` `flip--` `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` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 98

Calls

4 calls:

9.0ms	(+ (* y.re y.re) (* y.im y.im))
12.0ms	(- (* x.im y.re) (* x.re y.im))
21.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
51.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* y.re y.re) (* y.im y.im))
71.0ms	(- (* x.im y.re) (* x.re y.im))
72.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
108.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify3.3s

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
2	3275
1	421
0	140

prune669.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 28.4b

localize62.0ms

Local error

Found 4 expressions with local error:

17.6b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.9b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
34.9b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite44.0ms

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:

22.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
44.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
138.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
146.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify943.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1292
1	335
0	135

prune783.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 28.4b

regimes748.0ms

Accuracy

0% (3.2b remaining)

Error of 26.9b against oracle of 23.7b and baseline of 26.9b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample1.0s

Algorithm

intervals

Results

704.0ms

8480×

body

valid