Details

sample59.0ms

Algorithm

intervals

Results

43.0ms

272×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x.re y.re) (* x.im y.im))
0.0b	(+ (* y.re y.re) (* y.im y.im))
24.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite76.0ms

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:

12.0ms	(+ (* x.re y.re) (* x.im y.im))
12.0ms	(+ (* y.re y.re) (* y.im y.im))
52.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series201.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(+ (* x.re y.re) (* x.im y.im))
32.0ms	(+ (* y.re y.re) (* y.im y.im))
114.0ms	(/ (+ (* 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	2002
3	2002
2	1142
1	284
0	101

prune352.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`*-un-lft-identity` `add-cube-cbrt`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*` `flip3-+` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 268

Calls

4 calls:

64.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
38.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
139.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
53.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
58.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.4s

Counts

280 → 280

Iterations

Iter	Nodes
done	2010
3	2010
2	1755
1	724
0	305

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.5b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.im x.im) (* y.re x.re))
0.0b	(+ (* y.re y.re) (* y.im y.im))
24.6b	(/ (+ (* y.im x.im) (* y.re x.re)) (+ (* y.re y.re) (* y.im y.im)))

rewrite64.0ms

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:

13.0ms	(+ (* y.im x.im) (* y.re x.re))
16.0ms	(+ (* y.re y.re) (* y.im y.im))
34.0ms	(/ (+ (* y.im x.im) (* y.re x.re)) (+ (* y.re y.re) (* y.im y.im)))

series195.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* y.im x.im) (* y.re x.re))
33.0ms	(+ (* y.re y.re) (* y.im y.im))
123.0ms	(/ (+ (* y.im x.im) (* y.re x.re)) (+ (* y.re y.re) (* y.im y.im)))

simplify748.0ms

Counts

65 → 65

Iterations

Iter	Nodes
done	2002
3	2002
2	1003
1	279
0	98

prune247.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.im x.im) (* y.re x.re))
0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.im x.im) (* y.re x.re))))
24.2b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.im x.im) (* y.re x.re)))

rewrite381.0ms

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×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16`
2×	`+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `1-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 141

Calls

4 calls:

7.0ms	(+ (* y.im x.im) (* y.re x.re))
7.0ms	(+ (* y.re y.re) (* y.im y.im))
337.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.im x.im) (* y.re x.re))))
27.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.im x.im) (* y.re x.re)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (* y.im x.im) (* y.re x.re))
43.0ms	(+ (* y.re y.re) (* y.im y.im))
176.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.im x.im) (* y.re x.re))))
77.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* y.im x.im) (* y.re x.re)))

simplify997.0ms

Counts

153 → 153

Iterations

Iter	Nodes
done	2023
3	2023
2	1739
1	571
0	207

prune658.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.5b

regimes307.0ms

Accuracy

-0.2% (2.7b remaining)

Error of 26.1b against oracle of 23.4b and baseline of 26.1b

bsearch54.0ms

Steps

Iters	Range		Point
8	-8.814192133652473e+76	-1.2097032068419212e+74	-1.0148544823210362e+76

simplify5.0ms

Iterations

Iter	Nodes
done	24
1	24
0	18

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8489×

body

valid