Details

sample67.0ms

Algorithm

intervals

Results

45.0ms

269×

body

valid

simplify18.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	21
2	21
1	17
0	11

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.im y.im (* y.re y.re))
0.5b	(fma x.re y.re (* x.im y.im))
29.8b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite7.0ms

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` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 52

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

series252.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(fma y.im y.im (* y.re y.re))
69.0ms	(fma x.re y.re (* x.im y.im))
134.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify4.1s

Counts

61 → 61

Iterations

Iter	Nodes
5	6934
4	1865
3	562
2	236
1	116
0	76

prune852.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 29.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x.re y.re (* x.im y.im))
16.8b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
31.8b	(sqrt (fma y.im y.im (* y.re y.re)))
31.8b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite17.0ms

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` `insert-posit16` `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 → 87

Calls

4 calls:

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))))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(fma x.re y.re (* x.im y.im))
158.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
78.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
89.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify887.0ms

Counts

99 → 99

Iterations

Iter	Nodes
4	2543
3	824
2	293
1	142
0	93

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
0.5b	(fma x.re y.re (* x.im y.im))
16.8b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
31.8b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
96×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
25×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
6×	`div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `fma-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

26.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im 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)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
57.0ms	(fma x.re y.re (* x.im y.im))
130.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
53.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.4s

Counts

191 → 191

Iterations

Iter	Nodes
3	3593
2	1036
1	472
0	233

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.im y.re)
0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.5b	(fma x.re y.re (* x.im y.im))
16.8b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

rewrite17.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 125

Calls

4 calls:

0.0ms	(hypot y.im y.re)
9.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.0ms	(fma x.re y.re (* x.im y.im))
5.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

series415.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(hypot y.im y.re)
157.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
44.0ms	(fma x.re y.re (* x.im y.im))
131.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

simplify1.2s

Counts

137 → 137

Iterations

Iter	Nodes
3	3369
2	901
1	340
0	172

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

regimes313.0ms

Accuracy

32.9% (7.2b remaining)

Error of 12.9b against oracle of 5.7b and baseline of 16.4b

bsearch116.0ms

Steps

Iters	Range		Point
9	1.6933955445897368e+221	1.4196464610458346e+230	1.7195081298008246e+221
9	-4.2516442886911883e+123	-3.786455365439721e+118	-1.8277997780989823e+123

simplify3.0ms

Iterations

Iter	Nodes
2	20
1	20
0	18

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.5s

8488×

body

valid