Details

sample448.0ms

Algorithm

intervals

Results

67.0ms	76×	body	1280	valid
24.0ms	255×	body	80	valid
15.0ms	36×	body	640	valid
5.0ms	3×	body	2560	valid
4.0ms	16×	body	320	valid
2.0ms	7×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	35	21
1	63	17
2	98	17
3	217	17
4	895	17
5	5001	17
done	5001	17

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.im)
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`
1×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
172.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	213	458
1	565	417
2	1299	415
3	2889	415
4	5003	415
done	5003	415

prune384.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.1b

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.re)
1.4b	(* (atan2 x.im x.re) y.im)
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `flip-+` `hypot-def`

Counts

4 → 68

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (atan2 x.im x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
167.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify110.0ms

Counts

80 → 80

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	263	404
1	755	360
2	1828	359
3	4355	359
4	5001	359
done	5001	359

prune399.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.re)
1.4b	(* (atan2 x.im x.re) y.im)
5.8b	(exp (log (hypot x.re x.im)))
32.6b	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-sum`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-sum` `log-pow` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(exp (log (hypot x.re x.im)))
21.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
46.0ms	(exp (log (hypot x.re x.im)))
163.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify67.0ms

Counts

79 → 79

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	208	362
1	566	317
2	1248	317
3	2201	313
4	5001	313
done	5001	313

prune394.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.2b

localize33.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.re)
1.4b	(* (atan2 x.im x.re) y.im)
5.8b	(exp (log (hypot x.re x.im)))
32.6b	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-sum`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-sum` `log-pow` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(exp (log (hypot x.re x.im)))
21.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
46.0ms	(exp (log (hypot x.re x.im)))
165.0ms	(sin (+ (* (log (* 1 (hypot x.re x.im))) y.im) (* (atan2 x.im x.re) y.re)))

simplify66.0ms

Counts

79 → 79

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	208	362
1	566	317
2	1248	317
3	2201	313
4	5001	313
done	5001	313

prune378.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

regimes298.0ms

Accuracy

0% (0.1b remaining)

Error of 3.7b against oracle of 3.6b and baseline of 3.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	20
1	34	20
2	34	20
done	34	20

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	2307×	body	1280	valid
706.0ms	7933×	body	80	valid
592.0ms	1431×	body	640	valid
162.0ms	562×	body	320	valid
82.0ms	50×	body	2560	valid
46.0ms	247×	body	160	valid