Details

sample48.0ms

Algorithm

intervals

Results

22.0ms

277×

body

valid

simplify78.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	94
6	94
5	90
4	76
3	56
2	40
1	21
0	11

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize36.0ms

Local error

Found 2 expressions with local error:

0.8b	(fma (- y.im) x.re (* x.im y.re))
24.2b	(/ (fma (- y.im) x.re (* x.im y.re)) (fma y.im y.im (* y.re y.re)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

2 → 39

Calls

2 calls:

0.0ms	(fma (- y.im) x.re (* x.im y.re))
8.0ms	(/ (fma (- y.im) x.re (* x.im y.re)) (fma y.im y.im (* y.re y.re)))

series194.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(fma (- y.im) x.re (* x.im y.re))
126.0ms	(/ (fma (- y.im) x.re (* x.im y.re)) (fma y.im y.im (* y.re y.re)))

simplify1.1s

Counts

45 → 45

Iterations

Iter	Nodes
done	5001
3	1390
2	268
1	106
0	66

prune343.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.7b

localize31.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 1 (hypot y.re y.im)) (/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im)))
0.8b	(fma y.im (- x.re) (* x.im y.re))
16.4b	(/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`*-un-lft-identity` `add-exp-log`
25×	`add-cube-cbrt`
17×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
9×	`div-exp`
8×	`prod-exp`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`rec-exp` `1-exp`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef`

Counts

3 → 97

Calls

3 calls:

22.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im)))
0.0ms	(fma y.im (- x.re) (* x.im y.re))
4.0ms	(/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im))

series466.0ms

Counts

3 → 9

Calls

3 calls:

258.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im)))
64.0ms	(fma y.im (- x.re) (* x.im y.re))
144.0ms	(/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im))

simplify2.7s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	2357
1	375
0	141

prune730.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.1b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im)) (hypot y.re y.im))
0.8b	(fma y.im (- x.re) (* x.im y.re))
16.4b	(/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`fma-udef` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

14.0ms	(/ (/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im)) (hypot y.re y.im))
0.0ms	(fma y.im (- x.re) (* x.im y.re))
8.0ms	(/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im))

series437.0ms

Counts

3 → 9

Calls

3 calls:

175.0ms	(/ (/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im)) (hypot y.re y.im))
86.0ms	(fma y.im (- x.re) (* x.im y.re))
176.0ms	(/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im))

simplify905.0ms

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	1529
1	341
0	162

prune865.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 1 (/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re)))) (hypot y.re y.im))
0.2b	(/ 1 (/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re))))
0.8b	(fma (- y.im) x.re (* x.im y.re))
16.4b	(/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
50×	`associate-/l*`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`fma-udef` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 319

Calls

4 calls:

42.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re)))) (hypot y.re y.im))
17.0ms	(/ 1 (/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re))))
1.0ms	(fma (- y.im) x.re (* x.im y.re))
9.0ms	(/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re)))

series674.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re)))) (hypot y.re y.im))
227.0ms	(/ 1 (/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re))))
87.0ms	(fma (- y.im) x.re (* x.im y.re))
134.0ms	(/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re)))

simplify871.0ms

Counts

331 → 331

Iterations

Iter	Nodes
done	5000
1	1322
0	461

prune1.5s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.2b

regimes567.0ms

Accuracy

26.8% (10.3b remaining)

Error of 12.8b against oracle of 2.5b and baseline of 16.5b

bsearch108.0ms

Steps

Iters	Range		Point
7	1.501117643472263e+94	1.0344692428000016e+96	9.704509907519719e+95
9	-6.411730433752277e+138	-3.2464259169781065e+133	-2.3495253224574898e+135

simplify5.0ms

Iterations

Iter	Nodes
done	25
1	25
0	21

end0.0ms

sample1.3s

Algorithm

intervals

Results

785.0ms

8476×

body

valid