Details

sample474.0ms

Algorithm

intervals

Results

120.0ms	254×	body	80	valid
113.0ms	56×	body	1280	valid
66.0ms	46×	body	640	valid
26.0ms	21×	body	320	valid
5.0ms	7×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2059
6	2059
5	808
4	197
3	82
2	53
1	31
0	19

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize51.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (atan2 x.im x.re) y.im)
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite66.0ms

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:

5.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.im)
56.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
49.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
196.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts

72 → 72

Iterations

Iter	Nodes
done	2001
4	2001
3	911
2	425
1	202
0	99

prune624.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.6b

localize68.0ms

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)
2.1b	(* (atan2 x.im x.re) y.im)
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite55.0ms

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:

20.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
9.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
11.0ms	(* (atan2 x.im x.re) y.im)
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
128.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms	(* (atan2 x.im x.re) y.im)
52.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.4s

Counts

85 → 85

Iterations

Iter	Nodes
done	2005
4	2005
3	1753
2	685
1	297
0	137

prune559.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.9b

localize67.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (atan2 x.im x.re) y.im)
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite56.0ms

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:

6.0ms	(* (atan2 x.im x.re) y.im)
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 x.im x.re) y.im)
63.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
199.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	2001
4	2001
3	911
2	425
1	202
0	99

prune630.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.9b

localize116.0ms

Local error

Found 4 expressions with local error:

5.6b	(cbrt (* (atan2 x.im x.re) y.im))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt (* (atan2 x.im x.re) y.im))
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
47.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
189.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts

63 → 63

Iterations

Iter	Nodes
done	2000
5	2000
4	1675
3	734
2	361
1	195
0	100

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.9b

regimes587.0ms

Accuracy

64.8% (5.9b remaining)

Error of 9.2b against oracle of 3.4b and baseline of 20.0b

bsearch984.0ms

Steps

Iters	Range		Point
3	6.227311617042054e-62	8.126091106632713e-62	7.413330575436596e-62
9	3.583352435021582e-167	5.403831320372834e-158	1.3125844742081705e-162
9	-1.1974226794431701e-304	5.287973967575518e-307	4.682817159271393e-308
10	-1.7151696775463227e-21	-1.661845243425298e-34	-7.244640314977398e-31

simplify23.0ms

Iterations

Iter	Nodes
done	61
1	61
0	45

end0.0ms

sample10.6s

Algorithm

intervals

Results

4.6s	2089×	body	1280	valid
2.7s	8038×	body	80	valid
2.1s	1464×	body	640	valid
594.0ms	620×	body	320	valid
185.0ms	297×	body	160	valid