Details

sample374.0ms

Algorithm

intervals

Results

103.0ms	75×	body	1280	valid
73.0ms	18×	body	320	valid
59.0ms	263×	body	80	valid
41.0ms	43×	body	640	valid
4.0ms	10×	body	160	valid

simplify538.0ms

Counts: 1 → 1

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize74.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite70.0ms

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:

20.0ms	(* (atan2 x.im x.re) y.im)
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
23.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 x.im x.re) y.im)
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
221.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts: 68 → 68

prune521.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x.re x.re) (* x.im x.im))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.2b	(* (atan2 x.im x.re) y.im)
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

9.0ms	(+ (* x.re x.re) (* x.im x.im))
30.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
15.0ms	(* (atan2 x.im x.re) y.im)
18.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ (* x.re x.re) (* x.im x.im))
149.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
29.0ms	(* (atan2 x.im x.re) y.im)
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.3s

Counts: 77 → 77

prune461.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 2.0b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
0.2b	(* (log x.re) y.re)
2.2b	(* (atan2 x.im x.re) y.im)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`pow1`
7×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `add-cbrt-cube`
6×	`associate-r`
5×	`add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--`

Counts

3 → 49

Calls

3 calls:

9.0ms	(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
9.0ms	(* (log x.re) y.re)
13.0ms	(* (atan2 x.im x.re) y.im)

series283.0ms

Counts

3 → 9

Calls

3 calls:

148.0ms	(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
109.0ms	(* (log x.re) y.re)
26.0ms	(* (atan2 x.im x.re) y.im)

simplify1.4s

Counts: 58 → 58

prune232.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 2.0b

localize44.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite70.0ms

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:

14.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
57.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
210.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.5s

Counts: 68 → 68

prune553.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 2.0b

regimes317.0ms

Accuracy

70.7% (4.8b remaining)

Error of 8.2b against oracle of 3.4b and baseline of 19.7b

bsearch571.0ms

Steps

Iters	Range		Point
10	2.7200915701001408e-14	0.1320695871758506	0.019978299634689965
9	6.018728237912873e-122	7.894990393150501e-115	6.57893258982587e-122
10	-6.330883966516645e-307	2.451167048408795e-299	-2.14645045254987e-310

simplify1.3s

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.9s	2073×	body	1280	valid
1.9s	1409×	body	640	valid
1.7s	8016×	body	80	valid
407.0ms	651×	body	320	valid
143.0ms	317×	body	160	valid