Details

sample31.0ms

Algorithm

intervals

Results

14.0ms

277×

body

valid

simplify105.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize15.0ms

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)))

rewrite6.0ms

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))
4.0ms	(/ (fma (- y.im) x.re (* x.im y.re)) (fma y.im y.im (* y.re y.re)))

series191.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(fma (- y.im) x.re (* x.im y.re))
121.0ms	(/ (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

prune348.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.7b

localize17.0ms

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:

21.0ms	(* (/ 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))
8.0ms	(/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im))

series479.0ms

Counts

3 → 9

Calls

3 calls:

262.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im)))
70.0ms	(fma y.im (- x.re) (* x.im y.re))
147.0ms	(/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im))

simplify2.5s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	2357
1	375
0	141

prune713.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.1b

localize30.0ms

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))

rewrite23.0ms

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))
6.0ms	(/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im))

series444.0ms

Counts

3 → 9

Calls

3 calls:

212.0ms	(/ (/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im)) (hypot y.re y.im))
84.0ms	(fma y.im (- x.re) (* x.im y.re))
149.0ms	(/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im))

simplify950.0ms

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	1529
1	341
0	162

prune743.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.0b

localize32.0ms

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)))

rewrite89.0ms

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:

33.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re)))) (hypot y.re y.im))
21.0ms	(/ 1 (/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re))))
0.0ms	(fma (- y.im) x.re (* x.im y.re))
7.0ms	(/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re)))

series729.0ms

Counts

4 → 12

Calls

4 calls:

275.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re)))) (hypot y.re y.im))
225.0ms	(/ 1 (/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re))))
84.0ms	(fma (- y.im) x.re (* x.im y.re))
146.0ms	(/ (hypot y.re y.im) (fma (- y.im) x.re (* x.im y.re)))

simplify932.0ms

Counts

331 → 331

Iterations

Iter	Nodes
done	5000
1	1322
0	461

prune1.6s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.2b

regimes499.0ms

Accuracy

26.8% (10.3b remaining)

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

bsearch139.0ms

Steps

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

simplify3.0ms

Iterations

Iter	Nodes
done	25
1	25
0	21

end0.0ms

sample1.3s

Algorithm

intervals

Results

774.0ms

8476×

body

valid