Details

sample367.0ms

Algorithm

intervals

Results

38.0ms	65×	body	1280	valid
21.0ms	255×	body	80	valid
20.0ms	53×	body	640	valid
8.0ms	22×	body	320	valid
2.0ms	9×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

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: 6.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (atan2 x.im x.re) y.re)
0.5b	(/ (* (pow (hypot x.re x.im) y.re) (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
1.7b	(* (atan2 x.im x.re) y.im)
34.5b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-sqr-sqrt`
13×	`add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow-to-exp` `cos-sum` `frac-2neg` `pow-exp` `clear-num` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 75

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(/ (* (pow (hypot x.re x.im) y.re) (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
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)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
326.0ms	(/ (* (pow (hypot x.re x.im) y.re) (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
17.0ms	(* (atan2 x.im x.re) y.im)
162.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.8s

Counts

87 → 87

Iterations

Useful iterations: 3 (868.0ms)

Iter	Nodes	Cost
0	149	1444
1	321	1414
2	972	1207
3	4284	1200
done	5001	1200

prune361.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (atan2 x.im x.re) y.re)
0.5b	(/ (* (pow (hypot x.re x.im) y.re) (cbrt (pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3))) (exp (* (atan2 x.im x.re) y.im)))
1.7b	(* (atan2 x.im x.re) y.im)
34.5b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-sqr-sqrt`
12×	`add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow-to-exp` `cos-sum` `frac-2neg` `pow-exp` `clear-num` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 75

Calls

4 calls:

5.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(/ (* (pow (hypot x.re x.im) y.re) (cbrt (pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3))) (exp (* (atan2 x.im x.re) y.im)))
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)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.re)
321.0ms	(/ (* (pow (hypot x.re x.im) y.re) (cbrt (pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3))) (exp (* (atan2 x.im x.re) y.im)))
16.0ms	(* (atan2 x.im x.re) y.im)
147.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

87 → 87

Iterations

Useful iterations: 3 (884.0ms)

Iter	Nodes	Cost
0	153	1504
1	328	1366
2	996	1211
3	4463	1200
done	5001	1200

prune398.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (atan2 x.im x.re) y.re)
0.5b	(/ (* (pow (hypot x.re x.im) y.re) (cbrt (pow (log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))) 3))) (exp (* (atan2 x.im x.re) y.im)))
1.7b	(* (atan2 x.im x.re) y.im)
34.5b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-sqr-sqrt`
12×	`add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow-to-exp` `cos-sum` `frac-2neg` `pow-exp` `clear-num` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 75

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(/ (* (pow (hypot x.re x.im) y.re) (cbrt (pow (log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))) 3))) (exp (* (atan2 x.im x.re) y.im)))
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)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
307.0ms	(/ (* (pow (hypot x.re x.im) y.re) (cbrt (pow (log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))) 3))) (exp (* (atan2 x.im x.re) y.im)))
18.0ms	(* (atan2 x.im x.re) y.im)
143.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

87 → 87

Iterations

Useful iterations: 3 (881.0ms)

Iter	Nodes	Cost
0	154	1562
1	330	1366
2	998	1211
3	4468	1200
done	5000	1200

prune429.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.0b

localize25.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
34.5b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
34.5b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
34.5b	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite7.0ms

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:

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

series460.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
149.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
146.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
148.0ms	(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts

62 → 62

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	67	800
1	116	794
2	251	702
3	460	696
4	665	696
5	1149	696
6	2158	696
done	5001	696

prune341.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.0b

regimes277.0ms

Accuracy

48.9% (2.5b remaining)

Error of 6.2b against oracle of 3.7b and baseline of 8.5b

bsearch228.0ms

Steps

Iters	Range		Point
9	1.4399921914486052e-44	2.2458426208391953e-38	2.2221650931193274e-38
11	-1.710852101153785e+75	-1.0452457700408589e+52	-2.368427375727665e+74

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	88
1	35	63
done	35	63

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	2028×	body	1280	valid
676.0ms	8025×	body	80	valid
593.0ms	1534×	body	640	valid
190.0ms	690×	body	320	valid
54.0ms	305×	body	160	valid