Details

sample365.0ms

Algorithm

intervals

Results

37.0ms	62×	body	1280	valid
24.0ms	264×	body	80	valid
22.0ms	56×	body	640	valid
6.0ms	22×	body	320	valid
2.0ms	12×	body	160	valid

simplify680.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	19	37
1	31	37
2	53	36
3	84	36
4	201	36
5	851	36
done	5000	36

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (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)))
33.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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:

3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
159.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.7s

Counts

68 → 68

Iterations

Useful iterations: 3 (159.0ms)

Iter	Nodes	Cost
0	95	836
1	193	778
2	438	690
3	879	677
4	1750	677
5	4882	677
done	5000	677

prune308.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 17.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.5b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

10.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
92.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.4s

Counts

81 → 81

Iterations

Useful iterations: 4 (946.0ms)

Iter	Nodes	Cost
0	132	1042
1	282	985
2	704	871
3	1608	860
4	4854	859
done	5000	859

prune302.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (* (atan2 x.im x.re) y.im))
0.0b	(/ (pow (/ -1 x.re) (- y.re)) (exp (* (atan2 x.im x.re) y.im)))
0.5b	(* (atan2 x.im x.re) y.im)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

87×	`times-frac`
57×	`add-sqr-sqrt`
55×	`add-cube-cbrt` `*-un-lft-identity`
52×	`unpow-prod-down`
17×	`associate-/l*`
9×	`add-exp-log`
7×	`add-cbrt-cube`
5×	`pow1` `div-exp` `div-inv` `add-log-exp`
4×	`sqr-pow`
3×	`associate-r` `associate-l` `associate-/r*`
2×	`pow-exp` `associate-/l/`
1×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `pow-neg` `exp-prod` `exp-to-pow` `frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `rem-exp-log` `pow-sub` `unswap-sqr`

Counts

3 → 116

Calls

3 calls:

1.0ms	(exp (* (atan2 x.im x.re) y.im))
13.0ms	(/ (pow (/ -1 x.re) (- y.re)) (exp (* (atan2 x.im x.re) y.im)))
3.0ms	(* (atan2 x.im x.re) y.im)

series128.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(exp (* (atan2 x.im x.re) y.im))
91.0ms	(/ (pow (/ -1 x.re) (- y.re)) (exp (* (atan2 x.im x.re) y.im)))
16.0ms	(* (atan2 x.im x.re) y.im)

simplify532.0ms

Counts

125 → 125

Iterations

Useful iterations: 2 (171.0ms)

Iter	Nodes	Cost
0	254	2507
1	460	2409
2	1421	2334
done	5000	2334

prune422.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (- (log (pow (/ -1 x.re) (- y.re))) (* (atan2 x.im x.re) y.im)))
0.5b	(* (atan2 x.im x.re) y.im)
2.8b	(log (pow (/ -1 x.re) (- y.re)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

34×	`log-prod`
26×	`unpow-prod-down`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`exp-sum`
18×	`times-frac`
17×	`associate--l+`
9×	`add-exp-log`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
4×	`rem-log-exp`
3×	`exp-prod` `associate-r` `associate-l`
2×	`pow-neg` `log-div` `pow-exp` `div-inv` `rem-exp-log` `sqr-pow`
1×	`neg-sub0` `pow-to-exp` `sub-neg` `exp-diff` `diff-log` `div-exp` `log-rec` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `pow-sub` `unswap-sqr`

Counts

3 → 82

Calls

3 calls:

13.0ms	(exp (- (log (pow (/ -1 x.re) (- y.re))) (* (atan2 x.im x.re) y.im)))
3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(log (pow (/ -1 x.re) (- y.re)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(exp (- (log (pow (/ -1 x.re) (- y.re))) (* (atan2 x.im x.re) y.im)))
16.0ms	(* (atan2 x.im x.re) y.im)
89.0ms	(log (pow (/ -1 x.re) (- y.re)))

simplify2.2s

Counts

91 → 91

Iterations

Useful iterations: 3 (590.0ms)

Iter	Nodes	Cost
0	213	1293
1	434	1193
2	1068	1106
3	3642	1084
done	5000	1084

prune296.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.3b

regimes296.0ms

Accuracy

85.9% (2.3b remaining)

Error of 5.6b against oracle of 3.3b and baseline of 19.6b

bsearch196.0ms

Steps

Iters	Range		Point
9	9.165364975569095e-17	2.7654013913247297e-11	2.687600014275229e-11
10	-8.020324993682032e-16	-2.4313708196933896e-27	-7.937272784933259e-16

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	58
1	36	34
2	42	34
done	42	34

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	1989×	body	1280	valid
701.0ms	8076×	body	80	valid
553.0ms	1408×	body	640	valid
169.0ms	614×	body	320	valid
53.0ms	294×	body	160	valid