Details

sample41.0ms

Algorithm

intervals

Results

26.0ms

275×

body

valid

simplify60.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	70
5	70
4	66
3	48
2	36
1	19
0	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
27.2b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite51.0ms

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:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(- (* x.im y.re) (* x.re y.im))
35.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series196.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (* y.re y.re) (* y.im y.im))
57.0ms	(- (* x.im y.re) (* x.re y.im))
104.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts

67 → 67

Iterations

Iter	Nodes
3	4786
2	1199
1	304
0	104

prune771.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 26.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
14.4b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite48.0ms

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:

11.0ms	(- (* x.im y.re) (* x.re y.im))
22.0ms	(/ (- (* 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)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (* x.im y.re) (* x.re y.im))
150.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify963.0ms

Counts

102 → 102

Iterations

Iter	Nodes
3	2511
2	896
1	314
0	124

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
14.5b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
31.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.8b	(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` `add-cbrt-cube` `sqrt-div` `add-exp-log` `associate-/l*` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r*` `flip3-+` `flip-+`
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-exp` `div-inv`

Counts

4 → 89

Calls

4 calls:

14.0ms	(- (* x.im y.re) (* x.re y.im))
30.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* x.im y.re) (* x.re y.im))
90.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
46.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
60.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify765.0ms

Counts

101 → 101

Iterations

Iter	Nodes
3	2023
2	762
1	274
0	119

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
0.8b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
26.6b	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`div-exp` `add-log-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 142

Calls

4 calls:

7.0ms	(+ (* y.re y.re) (* y.im y.im))
7.0ms	(- (* x.im y.re) (* x.re y.im))
40.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
64.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (* y.re y.re) (* y.im y.im))
68.0ms	(- (* x.im y.re) (* x.re y.im))
205.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
75.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

simplify9.3s

Counts

154 → 154

Iterations

Iter	Nodes
3	6527
2	1690
1	568
0	211

prune1.6s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 24.5b

regimes383.0ms

Accuracy

0% (2.5b remaining)

Error of 25.7b against oracle of 23.2b and baseline of 25.7b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	18
1	18
0	15

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.0s

8499×

body

valid