Details

sample513.0ms

Algorithm

intervals

Results

113.0ms	256×	body	80	valid
80.0ms	43×	body	1280	valid
69.0ms	53×	body	640	valid
41.0ms	6×	body	160	valid
14.0ms	16×	body	320	valid

simplify3.2s

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize66.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.re)
29.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.re)
127.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
77.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
114.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (atan2 x.im x.re) y.re)
237.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
74.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
83.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.9s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
4	2040
3	865
2	415
1	201
0	101

prune707.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.7b

localize55.0ms

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)
0.9b	(* (atan2 x.im x.re) y.im)
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite358.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
20×	`associate-l`
13×	`pow1` `exp-prod`
10×	`add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
7×	`add-log-exp`
6×	`associate-r` `distribute-lft-out--` `unswap-sqr`
5×	`log-pow` `distribute-lft-out`
4×	`insert-posit16` `difference-of-squares`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `swap-sqr` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log`
1×	`rem-sqrt-square` `sub-neg` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 88

Calls

4 calls:

236.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
11.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
101.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
149.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
31.0ms	(* (atan2 x.im x.re) y.im)
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	1766
2	719
1	320
0	147

prune678.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.1b

localize111.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
33×	`associate-r`
22×	`cbrt-prod`
17×	`associate-l` `unswap-sqr`
16×	`add-cube-cbrt` `sqrt-prod`
14×	`add-cbrt-cube`
12×	`swap-sqr`
11×	`pow1`
10×	`distribute-lft-out`
9×	`add-exp-log` `cbrt-unprod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative`
2×	`rem-sqrt-square` `cos-sum` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`+-commutative`

Counts

4 → 109

Calls

4 calls:

77.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
79.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
75.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
775.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series468.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
236.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify2.2s

Counts

121 → 121

Iterations

Iter	Nodes
done	5001
3	2111
2	906
1	415
0	168

prune932.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.1b

localize101.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (* (cbrt y.re) (cbrt y.re)))))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (* (atan2 x.im x.re) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (* (cbrt y.re) (cbrt y.re))))) (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt y.re))))

rewrite27.0s

Algorithm

rewrite-expression-head

Rules

846×	`cbrt-prod`
822×	`add-sqr-sqrt`
511×	`unswap-sqr`
257×	`associate-r`
174×	`swap-sqr`
76×	`*-un-lft-identity`
67×	`associate-l`
53×	`*-commutative`
48×	`add-cube-cbrt`
16×	`sqrt-prod`
14×	`add-cbrt-cube`
11×	`pow1`
10×	`distribute-lft-out`
9×	`add-exp-log` `cbrt-unprod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp`
2×	`rem-sqrt-square` `cos-sum` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`+-commutative`

Counts

4 → 395

Calls

4 calls:

358.0ms	(* (atan2 x.im x.re) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (* (cbrt y.re) (cbrt y.re)))))
71.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
71.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.4s	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (* (atan2 x.im x.re) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (* (cbrt y.re) (cbrt y.re))))) (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt y.re))))

series620.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(* (atan2 x.im x.re) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (* (cbrt y.re) (cbrt y.re)))))
64.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
63.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
248.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (* (atan2 x.im x.re) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (* (cbrt y.re) (cbrt y.re))))) (cbrt (* (cbrt y.re) (cbrt y.re)))) (cbrt y.re))))

simplify2.7s

Counts

407 → 407

Iterations

Iter	Nodes
done	5000
2	2579
1	1068
0	424

prune2.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.1b

regimes627.0ms

Accuracy

62.9% (5.9b remaining)

Error of 9.3b against oracle of 3.4b and baseline of 19.4b

bsearch340.0ms

Steps

Iters	Range		Point
6	6.2956859368800825e-205	2.6609176224936472e-204	7.402062416285907e-205
8	-1.1392530337654849e-282	-2.574729366748541e-287	-8.138202357158243e-284

simplify14.0ms

Iterations

Iter	Nodes
done	43
1	43
0	33

end0.0ms

sample11.1s

Algorithm

intervals

Results

3.9s	1961×	body	1280	valid
3.0s	8009×	body	80	valid
2.0s	1444×	body	640	valid
1.6s	638×	body	320	valid
206.0ms	291×	body	160	valid