Details

sample38.0ms

Algorithm

intervals

Results

16.0ms

273×

body

valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	15	15
done	15	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(+ (* x.re y.re) (* x.im y.im))
27.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

20.0ms	(+ (* y.re y.re) (* y.im y.im))
12.0ms	(+ (* x.re y.re) (* x.im y.im))
46.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series239.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (* y.re y.re) (* y.im y.im))
54.0ms	(+ (* x.re y.re) (* x.im y.im))
142.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

62 → 62

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	99	1090
1	297	1067
2	1630	953
done	5001	951

prune392.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* 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))))
29.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `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` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

11.0ms	(+ (* x.re y.re) (* x.im y.im))
52.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ (* x.re y.re) (* x.im y.im))
174.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
67.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify937.0ms

Counts

96 → 96

Iterations

Useful iterations: done (932.0ms)

Iter	Nodes	Cost
0	117	1780
1	280	1649
2	1173	1543
done	5000	1541

prune732.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* 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))))
29.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `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` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

12.0ms	(+ (* x.re y.re) (* x.im y.im))
71.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (* x.re y.re) (* x.im y.im))
170.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
58.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
62.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify902.0ms

Counts

96 → 96

Iterations

Useful iterations: done (891.0ms)

Iter	Nodes	Cost
0	117	1780
1	280	1649
2	1173	1543
done	5000	1541

prune666.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im))))
0.7b	(+ (* y.re x.re) (* y.im x.im))
26.9b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`+-commutative` `rec-exp` `frac-2neg` `1-exp` `clear-num` `sum-log` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

12.0ms	(+ (* y.re y.re) (* y.im y.im))
35.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im))))
12.0ms	(+ (* y.re x.re) (* y.im x.im))
53.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* y.re y.re) (* y.im y.im))
224.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im))))
54.0ms	(+ (* y.re x.re) (* y.im x.im))
98.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.re x.re) (* y.im x.im)))

simplify2.8s

Counts

149 → 149

Iterations

Useful iterations: 2 (882.0ms)

Iter	Nodes	Cost
0	204	3676
1	588	3422
2	4197	3214
done	5002	3214

prune733.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 24.5b

regimes498.0ms

Accuracy

-6.3% (3.1b remaining)

Error of 26.5b against oracle of 23.3b and baseline of 26.3b

bsearch46.0ms

Steps

Iters	Range		Point
6	2.431590957525676e+49	1.8206035662555355e+50	1.0347324465362668e+50

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	39
1	21	39
done	21	39

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.4s

8471×

body

valid