Details

sample314.0ms

Algorithm

intervals

Results

98.0ms	250×	body	80	valid
70.0ms	55×	body	1280	valid
33.0ms	40×	body	640	valid
10.0ms	15×	body	320	valid
4.0ms	11×	body	160	valid

simplify4.4s

Counts

1 → 1

Iterations

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

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize354.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.im)
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite137.0ms

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×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

15.0ms	(* (atan2 x.im x.re) y.im)
27.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series724.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (atan2 x.im x.re) y.im)
85.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
88.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
490.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify5.7s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
4	2209
3	928
2	425
1	202
0	99

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.8b

localize164.0ms

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)
1.8b	(* (atan2 x.im x.re) y.im)
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

87.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
31.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
24.0ms	(* (atan2 x.im x.re) y.im)
30.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series649.0ms

Counts

4 → 12

Calls

4 calls:

302.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
220.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
49.0ms	(* (atan2 x.im x.re) y.im)
79.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify4.7s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	1739
2	674
1	297
0	137

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.4b

localize220.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x.re x.re) (* x.im x.im))
1.8b	(* (atan2 x.im x.re) y.im)
3.0b	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

35.0ms	(+ (* x.re x.re) (* x.im x.im))
15.0ms	(* (atan2 x.im x.re) y.im)
62.0ms	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (* x.re x.re) (* x.im x.im))
72.0ms	(* (atan2 x.im x.re) y.im)
68.0ms	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
54.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify4.8s

Counts

78 → 78

Iterations

Iter	Nodes
done	5002
3	1936
2	559
1	225
0	108

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize616.0ms

Local error

Found 4 expressions with local error:

31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
67.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
62.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
69.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series1.5s

Counts

4 → 12

Calls

4 calls:

85.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
473.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
424.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
501.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify8.4s

Counts

55 → 55

Iterations

Iter	Nodes
done	5003
5	3594
4	1189
3	539
2	265
1	141
0	70

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.3b

regimes1.7s

Accuracy

80% (6.2b remaining)

Error of 9.8b against oracle of 3.6b and baseline of 34.6b

bsearch902.0ms

Steps

Iters	Range		Point
9	3.0660807951351545e-33	4.403371930147517e-28	3.102132787630003e-33
7	1.4015695320788811e-64	1.0033532377411923e-62	9.798541471285326e-63
8	-6.28539424680076e-307	3.3383700148803893e-307	-1.91205330543206e-310
9	-1.0136022580229297e-153	-3.773586630999499e-162	-5.329546007764399e-159
6	-1.790535254998819e-16	-1.1589515176165432e-17	-4.64156243455413e-17

simplify55.0ms

Iterations

Iter	Nodes
done	75
1	75
0	56

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.8s	1988×	body	1280	valid
2.4s	7962×	body	80	valid
2.2s	1502×	body	640	valid
448.0ms	609×	body	320	valid
140.0ms	333×	body	160	valid