Details

sample54.0ms

Algorithm

intervals

Results

24.0ms

283×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 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)))

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

Counts

2 → 42

Calls

2 calls:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
52.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series203.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(+ (* x.re y.re) (* x.im y.im))
147.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.9s

Counts

48 → 48

Iterations

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

prune352.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.7b	(/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`*-un-lft-identity` `add-cube-cbrt`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*` `flip3-+` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 264

Calls

4 calls:

66.0ms	(/ (/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
45.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
160.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
62.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
46.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.4s

Counts

276 → 276

Iterations

Iter	Nodes
done	5000
2	3738
1	755
0	302

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* x.re y.re))))
14.7b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* x.re y.re)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
100×	`add-sqr-sqrt`
98×	`*-un-lft-identity` `add-cube-cbrt`
54×	`sqrt-prod`
27×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
9×	`associate-/l*`
8×	`flip3-+` `div-exp` `flip-+`
7×	`pow1`
6×	`sqrt-div` `div-inv`
4×	`cbrt-undiv` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 193

Calls

4 calls:

46.0ms	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* x.re y.re))))
18.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* x.re y.re)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* x.re y.re))))
121.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.im x.im) (* x.re y.re)))
53.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
64.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts

205 → 205

Iterations

Iter	Nodes
done	5001
2	3632
1	642
0	242

prune832.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.7b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x.im y.im) (* x.re y.re))
24.7b	(/ (+ (* x.im y.im) (* x.re y.re)) (+ (* y.re y.re) (* y.im y.im)))

rewrite50.0ms

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:

10.0ms	(+ (* x.im y.im) (* x.re y.re))
39.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (+ (* y.re y.re) (* y.im y.im)))

series174.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(+ (* x.im y.im) (* x.re y.re))
117.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
3	4320
2	906
1	237
0	86

prune260.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 20.7b

regimes522.0ms

Accuracy

-6.6% (3.7b remaining)

Error of 26.0b against oracle of 22.3b and baseline of 25.8b

bsearch56.0ms

Steps

Iters	Range		Point
9	-1.3194991668433843e+53	-7.867138586923555e+46	-1.3001792014151386e+53

simplify3.0ms

Iterations

Iter	Nodes
done	23
1	23
0	17

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.2s

8478×

body

valid