Details

sample376.0ms

Algorithm

intervals

Results

111.0ms	70×	body	1280	valid
46.0ms	255×	body	80	valid
43.0ms	53×	body	640	valid
5.0ms	11×	body	320	valid
3.0ms	8×	body	160	valid
2.0ms	1×	body	2560	valid

simplify4.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	808
4	197
3	82
2	53
1	31
0	19

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize139.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

10.0ms	(* (atan2 x.im x.re) y.im)
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
45.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series680.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (atan2 x.im x.re) y.im)
63.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
504.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.6s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
4	2214
3	916
2	421
1	207
0	102

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.9b

localize194.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite394.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum`

Counts

4 → 57

Calls

4 calls:

21.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
326.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
85.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
446.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify7.7s

Counts

69 → 69

Iterations

Iter	Nodes
done	5002
5	4306
4	1367
3	603
2	285
1	152
0	75

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.9b

localize198.0ms

Local error

Found 4 expressions with local error:

4.2b	(log (exp (* (atan2 x.im x.re) y.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-prod`
5×	`add-log-exp`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16`
3×	`log-prod` `log-pow`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`exp-prod` `exp-to-pow` `sin-sum` `rem-log-exp`

Counts

4 → 56

Calls

4 calls:

8.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series596.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
83.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
406.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify7.6s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
5	4427
4	1410
3	643
2	316
1	171
0	94

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.9b

localize284.0ms

Local error

Found 4 expressions with local error:

4.3b	(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`log-prod` `sqrt-prod`
5×	`add-exp-log`
4×	`add-cbrt-cube` `sqrt-div` `insert-posit16` `add-log-exp`
3×	`cbrt-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `log-pow` `flip-+`
1×	`sin-sum` `pow1/3` `rem-log-exp`

Counts

4 → 58

Calls

4 calls:

5.0ms	(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series729.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
70.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
421.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify7.3s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
5	3912
4	1318
3	623
2	323
1	184
0	105

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 19.9b

regimes1.5s

Accuracy

76.5% (3.4b remaining)

Error of 22.4b against oracle of 19.0b and baseline of 33.4b

bsearch531.0ms

Steps

Iters	Range	Point
4	-7.595307319507049e-306	-5.100675455252401e-306	-5.148958978483349e-306
8	-7.841047903969177e-156	-1.4042593121131706e-158	-4.748647839754185e-157
9	-4.352162551169737e-30	-1.4851173002701437e-39	-1.2685618014437514e-33

Iters

Range

Point

-7.595307319507049e-306

-5.100675455252401e-306

-5.148958978483349e-306

-7.841047903969177e-156

-1.4042593121131706e-158

-4.748647839754185e-157

-4.352162551169737e-30

-1.4851173002701437e-39

-1.2685618014437514e-33

simplify45.0ms

Iterations

Iter	Nodes
done	61
1	61
0	47

end0.0ms

sample9.1s

Algorithm

intervals

Results

4.4s	2218×	body	1280	valid
1.7s	7923×	body	80	valid
1.5s	1428×	body	640	valid
413.0ms	570×	body	320	valid
167.0ms	229×	body	160	valid
139.0ms	52×	body	2560	valid