Details

sample350.0ms

Algorithm

intervals

Results

123.0ms	61×	body	1280	valid
41.0ms	248×	body	80	valid
31.0ms	42×	body	640	valid
10.0ms	21×	body	320	valid
3.0ms	8×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1130
4	249
3	99
2	63
1	35
0	19

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize74.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
0.9b	(* (atan2 x.im x.re) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
32.9b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite35.0ms

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` `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 → 77

Calls

4 calls:

13.0ms	(* 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)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* y.re (log (hypot x.re x.im)))
20.0ms	(* (atan2 x.im x.re) y.re)
21.0ms	(* (atan2 x.im x.re) y.im)
236.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify981.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	871
1	270
0	138

prune938.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
0.9b	(* (atan2 x.im x.re) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
32.9b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite28.0ms

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` `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 → 77

Calls

4 calls:

12.0ms	(* 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)
2.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* y.re (log (hypot x.re x.im)))
29.0ms	(* (atan2 x.im x.re) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)
151.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify915.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	871
1	270
0	138

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize75.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
0.9b	(* (atan2 x.im x.re) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
32.9b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite47.0ms

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` `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 → 77

Calls

4 calls:

19.0ms	(* y.re (log (hypot x.re x.im)))
11.0ms	(* (atan2 x.im x.re) y.re)
11.0ms	(* (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)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* y.re (log (hypot x.re x.im)))
19.0ms	(* (atan2 x.im x.re) y.re)
27.0ms	(* (atan2 x.im x.re) y.im)
182.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	871
1	270
0	138

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize93.0ms

Local error

Found 4 expressions with local error:

7.8b	(cbrt (* (atan2 x.im x.re) y.re))
7.8b	(cbrt (* (atan2 x.im x.re) y.re))
7.8b	(cbrt (* (atan2 x.im x.re) y.re))
32.8b	(sin (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

rewrite20.0ms

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` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`sin-sum` `fma-udef`

Counts

4 → 43

Calls

4 calls:

5.0ms	(cbrt (* (atan2 x.im x.re) y.re))
5.0ms	(cbrt (* (atan2 x.im x.re) y.re))
5.0ms	(cbrt (* (atan2 x.im x.re) y.re))
4.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(cbrt (* (atan2 x.im x.re) y.re))
85.0ms	(cbrt (* (atan2 x.im x.re) y.re))
83.0ms	(cbrt (* (atan2 x.im x.re) y.re))
209.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

simplify1.3s

Counts

55 → 55

Iterations

Iter	Nodes
done	5001
4	1742
3	489
2	207
1	119
0	71

prune686.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

regimes666.0ms

Accuracy

0% (0.2b remaining)

Error of 3.5b against oracle of 3.3b and baseline of 3.5b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample9.1s

Algorithm

intervals

Results

3.3s	2261×	body	1280	valid
2.1s	1409×	body	640	valid
1.7s	8009×	body	80	valid
830.0ms	558×	body	320	valid
139.0ms	54×	body	2560	valid
93.0ms	244×	body	160	valid