Details

sample45.0ms

Algorithm

intervals

Results

23.0ms

273×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.5b	(+ (* x.re y.re) (* x.im y.im))
25.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite52.0ms

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))
18.0ms	(+ (* x.re y.re) (* x.im y.im))
25.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series187.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (* y.re y.re) (* y.im y.im))
48.0ms	(+ (* x.re y.re) (* x.im y.im))
94.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.3s

Counts

62 → 62

Iterations

Iter	Nodes
done	5005
3	4355
2	1069
1	281
0	98

prune413.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.2b

localize55.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (* x.re y.re) (* x.im y.im))
16.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite54.0ms

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:

6.0ms	(+ (* x.re y.re) (* x.im y.im))
26.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (* x.re y.re) (* x.im y.im))
124.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	5002
3	2699
2	906
1	280
0	117

prune540.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.8b

localize39.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (* x.re y.re) (* x.im y.im))
16.4b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
30.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/r*`
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:

6.0ms	(+ (* x.re y.re) (* x.im y.im))
19.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* x.re y.re) (* x.im y.im))
91.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
53.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
3	2261
2	797
1	270
0	115

prune755.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.8b

localize42.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (* x.re y.re) (* x.im y.im))
16.4b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
30.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
60.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (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)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (* x.re y.re) (* x.im y.im))
154.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
48.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.8s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
3	3643
2	1226
1	403
0	146

prune711.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.8b

regimes572.0ms

Accuracy

-3.4% (3.1b remaining)

Error of 26.7b against oracle of 23.6b and baseline of 26.6b

bsearch25.0ms

Steps

Iters	Range		Point
5	-2.2871888563215003e+52	-5.952772209436251e+51	-1.1491009642806413e+52

simplify6.0ms

Iterations

Iter	Nodes
done	24
1	24
0	18

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8459×

body

valid