Details

sample34.0ms

Algorithm

intervals

Results

16.0ms

271×

body

valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.2b	(+ (* x.re y.re) (* x.im y.im))
22.6b	(/ (+ (* 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:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
49.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series139.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+ (* x.re y.re) (* x.im y.im))
104.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts

48 → 48

Iterations

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

prune299.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 22.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* x.im y.im) (* x.re y.re))
14.2b	(/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite80.0ms

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.im y.im) (* x.re y.re))
44.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (* x.im y.im) (* x.re y.re))
166.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify619.0ms

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1173
1	280
0	117

prune591.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 20.6b

localize39.0ms

Local error

Found 4 expressions with local error:

14.2b	(/ (+ (* x.im y.im) (* x.re y.re)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

30×	`sqrt-div`
12×	`add-sqr-sqrt`
10×	`flip3-+` `flip-+`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod`
8×	`associate-/r/`
7×	`pow1`
4×	`frac-times` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `times-frac` `pow1/2` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-r/` `associate-/l/`
1×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

42.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts

88 → 88

Iterations

Iter	Nodes
done	5002
3	2637
2	812
1	279
0	107

prune643.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 20.6b

localize41.0ms

Local error

Found 4 expressions with local error:

14.2b	(/ (+ (* x.im y.im) (* x.re y.re)) (cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3)))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.8b	(cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

90×	`cbrt-prod`
63×	`times-frac`
59×	`add-sqr-sqrt`
57×	`*-un-lft-identity` `add-cube-cbrt`
36×	`sqrt-prod`
30×	`unpow-prod-down` `cube-prod`
21×	`associate-/r*`
8×	`sqrt-div`
6×	`pow1` `add-exp-log`
5×	`cube-mult` `flip3-+` `add-cbrt-cube` `unpow3` `flip-+` `sqr-pow`
4×	`cube-div` `cbrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/3` `div-exp` `rem-cbrt-cube` `div-inv`

Counts

4 → 162

Calls

4 calls:

48.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3))

series327.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3)))
59.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
60.0ms	(cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3))

simplify1.6s

Counts

174 → 174

Iterations

Iter	Nodes
done	5002
2	2546
1	431
0	188

prune1.1s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 20.6b

regimes577.0ms

Accuracy

0% (3.2b remaining)

Error of 26.7b against oracle of 23.5b and baseline of 26.7b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample1.0s

Algorithm

intervals

Results

707.0ms

8463×

body

valid