Details

sample65.0ms

Algorithm

intervals

Results

47.0ms

274×

body

valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	21
2	21
1	17
0	11

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.im y.im (* y.re y.re))
0.3b	(fma x.re y.re (* x.im y.im))
22.8b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma y.im y.im (* y.re y.re))
0.0ms	(fma x.re y.re (* x.im y.im))
4.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series247.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(fma y.im y.im (* y.re y.re))
69.0ms	(fma x.re y.re (* x.im y.im))
116.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify777.0ms

Counts

58 → 58

Iterations

Iter	Nodes
4	2394
3	722
2	268
1	115
0	73

prune686.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.4b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma x.re y.re (* x.im y.im))
12.8b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
27.6b	(sqrt (fma y.im y.im (* y.re y.re)))
27.6b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite7.0ms

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` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 83

Calls

4 calls:

0.0ms	(fma x.re y.re (* x.im y.im))
4.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma x.re y.re (* x.im y.im))
194.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
70.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
48.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.4s

Counts

95 → 95

Iterations

Iter	Nodes
5	4181
4	1477
3	531
2	237
1	137
0	90

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.7b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))))
0.3b	(fma x.re y.re (* x.im y.im))
12.8b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
27.6b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
57×	`times-frac`
43×	`*-un-lft-identity`
40×	`add-cube-cbrt`
28×	`add-exp-log`
27×	`sqrt-prod`
22×	`associate-r`
18×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp` `unswap-sqr`
8×	`prod-exp`
7×	`pow1`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `1-exp` `fma-udef`
1×	`frac-times` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `hypot-def`

Counts

4 → 137

Calls

4 calls:

37.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))))
0.0ms	(fma x.re y.re (* x.im y.im))
10.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
3.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series612.0ms

Counts

4 → 12

Calls

4 calls:

378.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))))
58.0ms	(fma x.re y.re (* x.im y.im))
125.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
50.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify5.1s

Counts

149 → 149

Iterations

Iter	Nodes
3	4871
2	1293
1	438
0	178

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.im y.re)
0.0b	(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.3b	(fma y.re x.re (* x.im y.im))
12.8b	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot y.im y.re)
12.0ms	(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.0ms	(fma y.re x.re (* x.im y.im))
4.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

series507.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(hypot y.im y.re)
167.0ms	(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
81.0ms	(fma y.re x.re (* x.im y.im))
180.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

simplify1.2s

Counts

133 → 133

Iterations

Iter	Nodes
3	3337
2	886
1	338
0	167

prune1.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.9b

regimes451.0ms

Accuracy

34.9% (7.0b remaining)

Error of 12.8b against oracle of 5.8b and baseline of 16.5b

bsearch156.0ms

Steps

Iters	Range		Point
9	3.811748495089899e+151	1.3867628498518926e+160	1.0408154521829639e+152
7	-1.482763807268155e+143	-4.987932973877915e+141	-6.24305058454472e+142

simplify6.0ms

Iterations

Iter	Nodes
2	20
1	20
0	18

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.5s

8465×

body

valid