Details

sample55.0ms

Algorithm

intervals

Results

37.0ms

272×

body

valid

simplify83.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.1b	(- (* x.im y.re) (* x.re y.im))
23.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite55.0ms

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:

14.0ms	(+ (* y.re y.re) (* y.im y.im))
14.0ms	(- (* x.im y.re) (* x.re y.im))
25.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series226.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (* y.re y.re) (* y.im y.im))
51.0ms	(- (* x.im y.re) (* x.re y.im))
136.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify855.0ms

Counts

67 → 67

Iterations

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

prune660.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 23.3b

localize28.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
13.7b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite73.0ms

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))
34.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
18.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* x.im y.re) (* x.re y.im))
149.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
43.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify816.0ms

Counts

102 → 102

Iterations

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

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.5b

localize65.0ms

Local error

Found 4 expressions with local error:

7.8b	(* (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
53×	`times-frac`
37×	`*-un-lft-identity`
33×	`associate-r` `add-cube-cbrt`
27×	`sqrt-prod`
26×	`add-exp-log`
18×	`cbrt-prod`
16×	`add-cbrt-cube`
13×	`associate-l`
12×	`unswap-sqr`
8×	`div-exp` `prod-exp`
7×	`pow1`
6×	`cbrt-div`
4×	`cbrt-undiv` `flip3-+` `sqrt-div` `cbrt-unprod` `flip-+` `insert-posit16` `add-log-exp`
2×	`rec-exp` `pow1/3` `1-exp` `associate-/r/` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 127

Calls

4 calls:

66.0ms	(* (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series798.0ms

Counts

4 → 12

Calls

4 calls:

544.0ms	(* (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
111.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
97.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

139 → 139

Iterations

Iter	Nodes
done	2003
2	2003
1	721
0	253

prune2.3s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 21.5b

localize68.0ms

Local error

Found 4 expressions with local error:

28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`sqrt-div`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 62

Calls

4 calls:

6.0ms	(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)))
8.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
64.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
104.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

74 → 74

Iterations

Iter	Nodes
done	2001
4	2001
3	1058
2	331
1	144
0	67

prune1.8s

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 21.5b

regimes651.0ms

Accuracy

0% (2.6b remaining)

Error of 25.3b against oracle of 22.7b and baseline of 25.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

8454×

body

valid