Details

sample356.0ms

Algorithm

intervals

Results

37.0ms	62×	body	1280	valid
24.0ms	264×	body	80	valid
22.0ms	56×	body	640	valid
6.0ms	22×	body	320	valid
2.0ms	12×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	19	37
1	35	26
2	63	25
3	98	25
4	215	25
5	859	25
done	5000	25

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
0.5b	(* (atan2 x.im x.re) y.re)
0.5b	(* (atan2 x.im x.re) y.im)
33.7b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

0.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
21.0ms	(* (atan2 x.im x.re) y.re)
18.0ms	(* (atan2 x.im x.re) y.im)
167.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.6s

Counts

72 → 72

Iterations

Useful iterations: 3 (214.0ms)

Iter	Nodes	Cost
0	101	729
1	177	720
2	409	634
3	852	630
4	1517	630
5	3614	630
done	5000	630

prune330.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3))
0.5b	(* (atan2 x.im x.re) y.re)
0.5b	(* (atan2 x.im x.re) y.im)
33.7b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`cbrt-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `cube-prod`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cube-mult` `cos-sum` `pow1/3` `unpow3` `rem-cbrt-cube` `fma-udef` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

1.0ms	(cbrt (pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3))
3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
1.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt (pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3))
17.0ms	(* (atan2 x.im x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
156.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

85 → 85

Iterations

Useful iterations: 3 (260.0ms)

Iter	Nodes	Cost
0	118	1167
1	215	1018
2	508	908
3	1107	904
4	2543	904
done	5000	904

prune408.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.0b

localize45.0ms

Local error

Found 4 expressions with local error:

3.5b	(cbrt (atan2 x.im x.re))
3.5b	(cbrt (atan2 x.im x.re))
3.5b	(cbrt (atan2 x.im x.re))
33.7b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt (atan2 x.im x.re))
0.0ms	(cbrt (atan2 x.im x.re))
0.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(cbrt (atan2 x.im x.re))
40.0ms	(cbrt (atan2 x.im x.re))
46.0ms	(cbrt (atan2 x.im x.re))
153.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.8s

Counts

61 → 61

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	54	529
1	82	516
2	134	456
3	229	445
4	516	445
5	1888	445
done	5001	445

prune341.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.0b

localize31.0ms

Local error

Found 4 expressions with local error:

3.5b	(cbrt (atan2 x.im x.re))
3.5b	(cbrt (atan2 x.im x.re))
3.5b	(cbrt (atan2 x.im x.re))
33.7b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt (atan2 x.im x.re))
0.0ms	(cbrt (atan2 x.im x.re))
0.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(cbrt (atan2 x.im x.re))
40.0ms	(cbrt (atan2 x.im x.re))
45.0ms	(cbrt (atan2 x.im x.re))
153.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

61 → 61

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	54	529
1	82	516
2	134	456
3	229	445
4	516	445
5	1888	445
done	5001	445

prune349.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.0b

regimes266.0ms

Accuracy

87.2% (0.4b remaining)

Error of 5.7b against oracle of 5.3b and baseline of 8.5b

bsearch4.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	129
1	51	129
done	51	129

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.2s	1989×	body	1280	valid
696.0ms	8076×	body	80	valid
557.0ms	1408×	body	640	valid
313.0ms	614×	body	320	valid
53.0ms	294×	body	160	valid