Details

sample527.0ms

Algorithm

intervals

Results

160.0ms	254×	body	80	valid
145.0ms	71×	body	1280	valid
73.0ms	39×	body	640	valid
9.0ms	14×	body	320	valid
9.0ms	4×	body	2560	valid
7.0ms	8×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2030
6	2030
5	823
4	210
3	95
2	62
1	35
0	19

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y.re (log (hypot x.re x.im)))
2.1b	(* (atan2 x.im x.re) y.re)
2.7b	(* (atan2 x.im x.re) y.im)
34.9b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
10×	`add-cbrt-cube` `associate-r` `add-exp-log`
9×	`associate-l`
6×	`log-prod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-sum` `log-pow` `fma-udef`

Counts

4 → 81

Calls

4 calls:

9.0ms	(* y.re (log (hypot x.re x.im)))
6.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* y.re (log (hypot x.re x.im)))
31.0ms	(* (atan2 x.im x.re) y.re)
31.0ms	(* (atan2 x.im x.re) y.im)
168.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.5s

Counts

93 → 93

Iterations

Iter	Nodes
done	2002
4	2002
3	1505
2	616
1	270
0	142

prune807.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.4b

localize70.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot x.re x.im))
2.1b	(* (atan2 x.im x.re) y.re)
2.7b	(* (atan2 x.im x.re) y.im)
34.9b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-sum` `pow1/3` `fma-udef`

Counts

4 → 67

Calls

4 calls:

1.0ms	(cbrt (hypot x.re x.im))
11.0ms	(* (atan2 x.im x.re) y.re)
12.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (hypot x.re x.im))
27.0ms	(* (atan2 x.im x.re) y.re)
31.0ms	(* (atan2 x.im x.re) y.im)
171.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts

79 → 79

Iterations

Iter	Nodes
done	2000
4	2000
3	1453
2	516
1	234
0	126

prune879.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.4b

localize101.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (atan2 x.im x.re) y.im)
34.9b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
34.9b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
34.9b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sin-sum` `associate-r` `associate-l` `fma-udef`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 54

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
5.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
5.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.im)
154.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
129.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
163.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts

66 → 66

Iterations

Iter	Nodes
done	2000
5	2000
4	1279
3	547
2	259
1	130
0	73

prune682.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.4b

localize88.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (atan2 x.im x.re) y.re)
2.7b	(* (atan2 x.im x.re) y.im)
34.9b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
60.0b	(posit16->real (real->posit16 (* y.re (log (hypot x.re x.im)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-sum` `fma-udef` `remove-posit16`

Counts

4 → 64

Calls

4 calls:

11.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
0.0ms	(posit16->real (real->posit16 (* y.re (log (hypot x.re x.im)))))

series353.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 x.im x.re) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)
177.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
126.0ms	(posit16->real (real->posit16 (* y.re (log (hypot x.re x.im)))))

simplify1.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	2003
4	2003
3	1176
2	454
1	207
0	114

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.4b

regimes592.0ms

Accuracy

0% (0.1b remaining)

Error of 3.5b against oracle of 3.4b and baseline of 3.5b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	27
1	27
0	21

end0.0ms

sample11.3s

Algorithm

intervals

Results

5.3s	2155×	body	1280	valid
2.5s	7955×	body	80	valid
2.0s	1395×	body	640	valid
605.0ms	542×	body	320	valid
219.0ms	49×	body	2560	valid
214.0ms	252×	body	160	valid