Details

sample644.0ms

Algorithm

intervals

Results

92.0ms	65×	body	1280	valid
57.0ms	257×	body	80	valid
44.0ms	43×	body	640	valid
8.0ms	12×	body	320	valid
4.0ms	8×	body	160	valid
3.0ms	1×	body	2560	valid

simplify2.5s

Counts

1 → 1

Iterations

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

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
0.8b	(* (atan2 x.im x.re) y.re)
1.8b	(* (atan2 x.im x.re) y.im)
31.3b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

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:

7.0ms	(* y.re (log (hypot x.re x.im)))
5.0ms	(* (atan2 x.im x.re) y.re)
5.0ms	(* (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)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* y.re (log (hypot x.re x.im)))
32.0ms	(* (atan2 x.im x.re) y.re)
26.0ms	(* (atan2 x.im x.re) y.im)
189.0ms	(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

prune938.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

localize75.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (* (atan2 x.im x.re) y.im))
5.7b	(cbrt (* (atan2 x.im x.re) y.im))
5.7b	(cbrt (* (atan2 x.im x.re) y.im))
31.3b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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:

12.0ms	(cbrt (* (atan2 x.im x.re) y.im))
4.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (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)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (* (atan2 x.im x.re) y.im))
81.0ms	(cbrt (* (atan2 x.im x.re) y.im))
100.0ms	(cbrt (* (atan2 x.im x.re) y.im))
202.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

55 → 55

Iterations

Iter	Nodes
done	5002
4	1845
3	485
2	209
1	121
0	72

prune738.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

localize157.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (* (atan2 x.im x.re) y.im))
5.7b	(cbrt (* (atan2 x.im x.re) y.im))
5.7b	(cbrt (* (atan2 x.im x.re) y.im))
31.3b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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.im))
5.0ms	(cbrt (* (atan2 x.im x.re) y.im))
6.0ms	(cbrt (* (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)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(cbrt (* (atan2 x.im x.re) y.im))
89.0ms	(cbrt (* (atan2 x.im x.re) y.im))
101.0ms	(cbrt (* (atan2 x.im x.re) y.im))
159.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.5s

Counts

55 → 55

Iterations

Iter	Nodes
done	5002
4	1845
3	485
2	209
1	121
0	72

prune924.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

localize183.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (* (atan2 x.im x.re) y.im))
5.7b	(cbrt (* (atan2 x.im x.re) y.im))
5.7b	(cbrt (* (atan2 x.im x.re) y.im))
31.3b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite11.0ms

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:

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

series502.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (* (atan2 x.im x.re) y.im))
123.0ms	(cbrt (* (atan2 x.im x.re) y.im))
95.0ms	(cbrt (* (atan2 x.im x.re) y.im))
183.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts

55 → 55

Iterations

Iter	Nodes
done	5002
4	1845
3	485
2	209
1	121
0	72

prune773.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

regimes723.0ms

Accuracy

0% (0.1b remaining)

Error of 3.6b against oracle of 3.6b and baseline of 3.6b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	27
1	27
0	21

end0.0ms

sample8.8s

Algorithm

intervals

Results

4.1s	2237×	body	1280	valid
2.2s	7951×	body	80	valid
1.3s	1455×	body	640	valid
365.0ms	584×	body	320	valid
119.0ms	47×	body	2560	valid
81.0ms	235×	body	160	valid