Details

sample60.0ms

Algorithm

intervals

Results

41.0ms

267×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	21
2	21
1	17
0	11

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize27.0ms

Local error

Found 2 expressions with local error:

0.5b	(fma x.re y.re (* x.im y.im))
26.9b	(/ (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

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

Counts

2 → 41

Calls

2 calls:

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

series187.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(fma x.re y.re (* x.im y.im))
138.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify1.2s

Counts

47 → 47

Iterations

Iter	Nodes
4	3311
3	932
2	294
1	106
0	67

prune722.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x.re y.re (* x.im y.im))
18.2b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
29.2b	(sqrt (fma y.im y.im (* y.re y.re)))
29.2b	(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)))
3.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(fma x.re y.re (* x.im y.im))
186.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
64.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
85.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify999.0ms

Counts

99 → 99

Iterations

Iter	Nodes
4	2628
3	853
2	305
1	143
0	93

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
0.5b	(fma x.re y.re (* x.im y.im))
18.2b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
29.2b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
91×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `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 → 173

Calls

4 calls:

9.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re 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))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series550.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
54.0ms	(fma x.re y.re (* x.im y.im))
173.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
78.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.2s

Counts

185 → 185

Iterations

Iter	Nodes
3	3273
2	1058
1	455
0	232

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.8b

localize22.0ms

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))
18.2b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

rewrite19.0ms

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)
12.0ms	(/ (/ (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))

series469.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(hypot y.im y.re)
174.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
67.0ms	(fma x.re y.re (* x.im y.im))
164.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

simplify1.2s

Counts

137 → 137

Iterations

Iter	Nodes
3	3336
2	887
1	341
0	172

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

regimes360.0ms

Accuracy

16.1% (8.9b remaining)

Error of 14.6b against oracle of 5.7b and baseline of 16.3b

bsearch81.0ms

Steps

Iters	Range		Point
9	1.5003900196443502e+89	1.3503841771177545e+95	9.936266958075772e+94

simplify4.0ms

Iterations

Iter	Nodes
2	18
1	18
0	15

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.7s

8467×

body

valid