Details

sample70.0ms

Algorithm

intervals

Results

51.0ms

277×

body

valid

simplify61.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	70
5	70
4	66
3	48
2	36
1	19
0	11

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.5b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.0b	(- (* x.im y.re) (* x.re y.im))
24.5b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite38.0ms

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`
3×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 58

Calls

3 calls:

10.0ms	(+ (* y.re y.re) (* y.im y.im))
7.0ms	(- (* x.im y.re) (* x.re y.im))
20.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series225.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (* y.re y.re) (* y.im y.im))
68.0ms	(- (* x.im y.re) (* x.re y.im))
124.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify897.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	2001
3	2001
2	1186
1	305
0	104

prune728.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.1b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* x.im y.re) (* x.re y.im))
14.3b	(/ (- (* x.im y.re) (* x.re 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)))

rewrite45.0ms

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`
4×	`insert-posit16`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 90

Calls

4 calls:

7.0ms	(- (* x.im y.re) (* x.re y.im))
21.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* x.im y.re) (* x.re y.im))
133.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
58.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts

102 → 102

Iterations

Iter	Nodes
done	2000
3	2000
2	934
1	315
0	124

prune516.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.1b

localize45.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* x.im y.re) (* x.re y.im))
14.4b	(* (- (* x.im y.re) (* x.re 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)))

rewrite74.0ms

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×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp` `insert-posit16`
3×	`flip3-+` `flip3--` `associate-l` `flip-+` `flip--`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `sub-neg` `diff-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 99

Calls

4 calls:

7.0ms	(- (* x.im y.re) (* x.re y.im))
41.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* x.im y.re) (* x.re y.im))
141.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
58.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts

111 → 111

Iterations

Iter	Nodes
done	2002
3	2002
2	1129
1	397
0	151

prune545.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.6b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
1.0b	(- (* x.im y.re) (* x.re y.im))
24.4b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite66.0ms

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`
4×	`div-exp` `prod-exp` `associate-/r/` `insert-posit16`
3×	`associate-/r` `flip3-+` `flip3--` `associate-l` `flip-+` `flip--` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 102

Calls

4 calls:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
12.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(- (* x.im y.re) (* x.re y.im))
38.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* y.re y.re) (* y.im y.im))
60.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
70.0ms	(- (* x.im y.re) (* x.re y.im))
146.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify1.1s

Counts

114 → 114

Iterations

Iter	Nodes
done	2000
3	2000
2	1576
1	406
0	144

prune482.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 23.1b

regimes467.0ms

Accuracy

0% (2.3b remaining)

Error of 25.3b against oracle of 23.0b and baseline of 25.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8503×

body

valid