Details

sample348.0ms

Algorithm

intervals

Results

126.0ms	56×	body	1280	valid
55.0ms	254×	body	80	valid
46.0ms	46×	body	640	valid
17.0ms	21×	body	320	valid
4.0ms	7×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
1.6b	(* (atan2 x.im x.re) y.re)
2.1b	(* (atan2 x.im x.re) y.im)
32.7b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite33.0ms

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×	`cos-sum` `log-pow` `fma-udef`

Counts

4 → 81

Calls

4 calls:

7.0ms	(* 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)
11.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* y.re (log (hypot x.re x.im)))
33.0ms	(* (atan2 x.im x.re) y.re)
30.0ms	(* (atan2 x.im x.re) y.im)
177.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify977.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	2002
3	2002
2	736
1	298
0	150

prune892.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
1.6b	(* (atan2 x.im x.re) y.re)
2.1b	(* (atan2 x.im x.re) y.im)
32.7b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

4.0ms	(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
6.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
29.0ms	(* (atan2 x.im x.re) y.re)
22.0ms	(* (atan2 x.im x.re) y.im)
160.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts

84 → 84

Iterations

Iter	Nodes
done	2005
4	2005
3	1470
2	553
1	245
0	133

prune709.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.0b

localize77.0ms

Local error

Found 4 expressions with local error:

5.6b	(cbrt (* (atan2 x.im x.re) y.im))
5.6b	(cbrt (* (atan2 x.im x.re) y.im))
5.6b	(cbrt (* (atan2 x.im x.re) y.im))
32.7b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 47

Calls

4 calls:

3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
2.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(cbrt (* (atan2 x.im x.re) y.im))
74.0ms	(cbrt (* (atan2 x.im x.re) y.im))
111.0ms	(cbrt (* (atan2 x.im x.re) y.im))
180.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts

59 → 59

Iterations

Iter	Nodes
done	2007
4	2007
3	675
2	293
1	151
0	83

prune739.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.0b

localize111.0ms

Local error

Found 4 expressions with local error:

5.6b	(cbrt (* (atan2 x.im x.re) y.im))
5.6b	(cbrt (* (atan2 x.im x.re) y.im))
5.6b	(cbrt (* (atan2 x.im x.re) y.im))
32.7b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 47

Calls

4 calls:

3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
7.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (* (atan2 x.im x.re) y.im))
67.0ms	(cbrt (* (atan2 x.im x.re) y.im))
64.0ms	(cbrt (* (atan2 x.im x.re) y.im))
147.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts

59 → 59

Iterations

Iter	Nodes
done	2007
4	2007
3	675
2	293
1	151
0	83

prune998.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.0b

regimes531.0ms

Accuracy

0% (0.0b remaining)

Error of 3.4b against oracle of 3.3b and baseline of 3.4b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample10.8s

Algorithm

intervals

Results

4.7s	2089×	body	1280	valid
2.5s	8038×	body	80	valid
2.4s	1464×	body	640	valid
613.0ms	620×	body	320	valid
211.0ms	297×	body	160	valid