Details

sample539.0ms

Algorithm

intervals

Results

189.0ms	88×	body	1280	valid
64.0ms	58×	body	640	valid
56.0ms	256×	body	80	valid
13.0ms	20×	body	320	valid
6.0ms	13×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	19	37
1	35	26
2	63	25
3	99	25
4	232	25
5	1034	25
done	5000	25

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
1.0b	(* (atan2 x.im x.re) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
31.2b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite42.0ms

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:

1.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
15.0ms	(* (atan2 x.im x.re) y.re)
15.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
29.0ms	(* (atan2 x.im x.re) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)
280.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify4.8s

Counts

72 → 72

Iterations

Useful iterations: 3 (998.0ms)

Iter	Nodes	Cost
0	101	729
1	182	720
2	576	638
3	4394	630
done	5000	630

prune519.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3)
1.0b	(* (atan2 x.im x.re) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
31.2b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`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` `pow-unpow` `cube-prod`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `cos-sum` `pow-pow` `unpow3` `pow-exp` `fma-udef` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

4.0ms	(pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3)
11.0ms	(* (atan2 x.im x.re) y.re)
14.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

381.0ms	(pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3)
26.0ms	(* (atan2 x.im x.re) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
233.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify980.0ms

Counts

87 → 87

Iterations

Useful iterations: done (976.0ms)

Iter	Nodes	Cost
0	117	1100
1	280	1018
2	1114	910
done	5001	906

prune617.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize43.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
31.2b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
31.2b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
31.2b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
2.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
3.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series744.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 x.im x.re) y.im)
242.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
243.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
228.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.6s

Counts

62 → 62

Iterations

Useful iterations: 3 (504.0ms)

Iter	Nodes	Cost
0	67	800
1	120	794
2	359	702
3	2404	696
done	5000	696

prune918.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.9b

localize45.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) y.re)
1.0b	(* (atan2 x.im x.re) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
31.7b	(cos (* (* (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

10.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(* (atan2 x.im x.re) y.im)
48.0ms	(cos (* (* (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 x.im x.re) y.re)
20.0ms	(* (atan2 x.im x.re) y.re)
29.0ms	(* (atan2 x.im x.re) y.im)
262.0ms	(cos (* (* (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))

simplify5.6s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	85	1008
1	161	998
2	541	624
3	4569	588
done	5000	588

prune695.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.9b

regimes470.0ms

Accuracy

74.5% (0.8b remaining)

Error of 6.5b against oracle of 5.7b and baseline of 8.9b

bsearch7.0ms

simplify14.0ms

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	31	94
1	41	91
2	43	89
done	43	89

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.4s	2048×	body	1280	valid
1.8s	7982×	body	80	valid
1.4s	1511×	body	640	valid
847.0ms	612×	body	320	valid
100.0ms	305×	body	160	valid