Details

sample50.0ms

Algorithm

intervals

Results

34.0ms

263×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize52.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.8b	(+ (* x.re y.re) (* x.im y.im))
27.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite46.0ms

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` `insert-posit16` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 56

Calls

3 calls:

11.0ms	(+ (* y.re y.re) (* y.im y.im))
7.0ms	(+ (* x.re y.re) (* x.im y.im))
27.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series195.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (* y.re y.re) (* y.im y.im))
58.0ms	(+ (* x.re y.re) (* x.im y.im))
103.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

65 → 65

Iterations

Iter	Nodes
done	5002
2	1730
1	300
0	101

prune368.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 26.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* x.re y.re) (* x.im y.im))
18.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.3b	(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-+`
4×	`insert-posit16`
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 → 88

Calls

4 calls:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
28.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (* x.re y.re) (* x.im y.im))
119.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1126
1	283
0	120

prune533.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* y.im x.im) (* y.re x.re))
18.4b	(/ (+ (* y.im x.im) (* y.re x.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite58.0ms

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-+`
4×	`insert-posit16`
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 → 88

Calls

4 calls:

11.0ms	(+ (* y.im x.im) (* y.re x.re))
34.0ms	(/ (+ (* y.im x.im) (* y.re x.re)) (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)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (* y.im x.im) (* y.re x.re))
120.0ms	(/ (+ (* y.im x.im) (* y.re x.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
43.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify808.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1024
1	281
0	117

prune563.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 23.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* x.re y.re) (* x.im y.im))
18.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite95.0ms

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-+`
4×	`insert-posit16`
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 → 88

Calls

4 calls:

14.0ms	(+ (* x.re y.re) (* x.im y.im))
61.0ms	(/ (+ (* 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)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* x.re y.re) (* x.im y.im))
163.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
64.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify958.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1126
1	283
0	120

prune653.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.7b

regimes505.0ms

Accuracy

0% (3.6b remaining)

Error of 26.2b against oracle of 22.6b and baseline of 26.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.5s

8425×

body

valid