Details

sample41.0ms

Algorithm

intervals

Results

20.0ms

270×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
24.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite59.0ms

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`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 53

Calls

3 calls:

9.0ms	(+ (* y.re y.re) (* y.im y.im))
16.0ms	(+ (* x.re y.re) (* x.im y.im))
32.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series158.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* y.re y.re) (* y.im y.im))
35.0ms	(+ (* x.re y.re) (* x.im y.im))
93.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify926.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
2	1625
1	296
0	98

prune360.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
16.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b	(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`
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:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
31.0ms	(/ (+ (* 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)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (* x.re y.re) (* x.im y.im))
140.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
50.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify982.0ms

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1173
1	280
0	117

prune631.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
24.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

6.0ms	(+ (* x.re y.re) (* x.im y.im))
57.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (+ (* y.re y.re) (* y.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)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* x.re y.re) (* x.im y.im))
87.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (+ (* y.re y.re) (* y.im y.im))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts

84 → 84

Iterations

Iter	Nodes
done	5002
3	3292
2	934
1	294
0	113

prune583.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
0.5b	(+ (* x.re y.re) (* x.im y.im))
24.7b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite67.0ms

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`
6×	`flip3-+` `flip-+`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-/r` `associate-l` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 97

Calls

4 calls:

6.0ms	(+ (* y.re y.re) (* y.im y.im))
11.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(+ (* x.re y.re) (* x.im y.im))
39.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series222.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* y.re y.re) (* y.im y.im))
49.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(+ (* x.re y.re) (* x.im y.im))
93.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify2.7s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	3630
1	430
0	139

prune505.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 22.8b

regimes451.0ms

Accuracy

0% (3.0b remaining)

Error of 26.0b against oracle of 23.1b and baseline of 26.0b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.0s

8493×

body

valid