Details

sample448.0ms

Algorithm

intervals

Results

44.0ms	76×	body	1280	valid
36.0ms	34×	body	640	valid
23.0ms	254×	body	80	valid
6.0ms	21×	body	320	valid
2.0ms	8×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20
done	5001	20

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.2b

localize28.0ms

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)))
32.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite50.0ms

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×	`sqrt-div` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

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)))
25.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
163.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify73.0ms

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	191	420
1	501	383
2	1134	381
3	2496	381
4	5001	381
done	5001	381

prune303.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.4b	(* (atan2 x.im x.re) y.im)
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-r`
3×	`exp-prod` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 69

Calls

4 calls:

20.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
12.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
9.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
94.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms	(* (atan2 x.im x.re) y.im)
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify56.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	280	545
1	825	486
2	2118	481
3	5001	481
done	5001	481

prune269.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (exp (* (atan2 x.im x.re) y.im)))
1.4b	(* (atan2 x.im x.re) y.im)
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`times-frac`
29×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
15×	`sqrt-prod`
10×	`associate-/l*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`sqr-pow`
3×	`div-exp` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
2×	`sqrt-div`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`

Counts

3 → 90

Calls

3 calls:

34.0ms	(/ (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (exp (* (atan2 x.im x.re) y.im)))
7.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series178.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(/ (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (exp (* (atan2 x.im x.re) y.im)))
18.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify108.0ms

Counts

99 → 99

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	345	1143
1	1124	1082
2	4650	1079
3	5001	1078
done	5001	1078

prune313.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.4b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
11×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 69

Calls

4 calls:

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

series93.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(* (atan2 x.im x.re) y.im)
21.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify64.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	145	322
1	428	289
2	1017	288
3	2145	288
4	5002	288
done	5002	288

prune280.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.4b

regimes235.0ms

Accuracy

54.8% (6.9b remaining)

Error of 11.3b against oracle of 4.4b and baseline of 19.7b

bsearch447.0ms

Steps

Iters	Range		Point
10	7.704108445868586e-11	33183.92535515244	0.049666903313089414
10	2.67271266005654e-166	2.2896112546321894e-155	8.333241630915609e-157
9	-1.2772633849980886e-303	5.690367183293641e-307	-2.4485621286449e-310
10	-2.75541712276274e-251	-1.6878141620607126e-261	-8.512054391915102e-257

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	43
1	62	43
2	65	43
3	65	43
done	65	43

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.2s	2143×	body	1280	valid
680.0ms	7948×	body	80	valid
560.0ms	1451×	body	640	valid
182.0ms	669×	body	320	valid
62.0ms	319×	body	160	valid