Details

sample31.0ms

Algorithm

intervals

Results

14.0ms

262×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.3b

localize11.0ms

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))
21.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite83.0ms

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:

16.0ms	(+ (* y.re y.re) (* y.im y.im))
15.0ms	(+ (* 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)))

series228.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ (* y.re y.re) (* y.im y.im))
42.0ms	(+ (* x.re y.re) (* x.im y.im))
138.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify865.0ms

Counts

62 → 62

Iterations

Useful iterations: done (862.0ms)

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

prune253.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
14.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (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)))

rewrite65.0ms

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:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
39.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* x.re y.re) (* x.im y.im))
127.0ms	(/ (+ (* 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)))
43.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify856.0ms

Counts

96 → 96

Iterations

Useful iterations: done (846.0ms)

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

prune381.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 18.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
14.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (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)))

rewrite108.0ms

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:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
64.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(+ (* x.re y.re) (* x.im y.im))
183.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
71.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify941.0ms

Counts

96 → 96

Iterations

Useful iterations: done (936.0ms)

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

prune491.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 18.4b

localize25.0ms

Local error

Found 4 expressions with local error:

14.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (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)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`sqrt-prod`
18×	`times-frac`
8×	`sqrt-div`
7×	`pow1`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 88

Calls

4 calls:

53.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
67.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.6s

Counts

100 → 100

Iterations

Useful iterations: 3 (907.0ms)

Iter	Nodes	Cost
0	105	1833
1	249	1680
2	895	1572
3	4467	1548
done	5001	1548

prune580.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 18.4b

regimes342.0ms

Accuracy

14.2% (2.4b remaining)

Error of 25.8b against oracle of 23.4b and baseline of 26.2b

bsearch4.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	54
1	25	54
done	25	54

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.1s

8441×

body

valid