Details

sample430.0ms

Algorithm

intervals

Results

52.0ms	54×	body	1280	valid
23.0ms	259×	body	80	valid
16.0ms	41×	body	640	valid
5.0ms	16×	body	320	valid
1.0ms	8×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	21
1	63	17
2	98	17
3	217	17
4	895	17
5	5001	17
done	5001	17

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize26.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.re)
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite53.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.re)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(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)))

simplify77.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	205	454
1	546	413
2	1264	411
3	2748	411
4	5001	411
done	5001	411

prune360.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (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)
1.9b	(* (atan2 x.im x.re) y.im)
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite38.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `fma-neg` `diff-log` `prod-diff` `flip--` `flip-+` `hypot-def`

Counts

4 → 77

Calls

4 calls:

9.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
12.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
90.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify82.0ms

Counts

89 → 89

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	320	595
1	1020	544
2	3156	516
3	5001	484
done	5001	484

prune309.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.re)
0.6b	(cbrt y.re)
0.6b	(cbrt y.re)
1.9b	(* (atan2 x.im x.re) y.im)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-r` `associate-l`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

1.0ms	(cbrt y.re)
1.0ms	(cbrt y.re)
1.0ms	(cbrt y.re)
7.0ms	(* (atan2 x.im x.re) y.im)

series545.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt y.re)
173.0ms	(cbrt y.re)
174.0ms	(cbrt y.re)
21.0ms	(* (atan2 x.im x.re) y.im)

simplify55.0ms

Counts

71 → 71

Iterations

Useful iterations: 3 (19.0ms)

Iter	Nodes	Cost
0	102	209
1	300	190
2	710	184
3	1530	181
4	5001	181
done	5001	181

prune292.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.re)
0.6b	(cbrt y.re)
0.6b	(cbrt y.re)
1.9b	(* (atan2 x.im x.re) y.im)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-r` `associate-l`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

1.0ms	(cbrt y.re)
1.0ms	(cbrt y.re)
1.0ms	(cbrt y.re)
7.0ms	(* (atan2 x.im x.re) y.im)

series548.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt y.re)
174.0ms	(cbrt y.re)
175.0ms	(cbrt y.re)
18.0ms	(* (atan2 x.im x.re) y.im)

simplify54.0ms

Counts

71 → 71

Iterations

Useful iterations: 3 (18.0ms)

Iter	Nodes	Cost
0	102	209
1	300	190
2	710	184
3	1530	181
4	5001	181
done	5001	181

prune317.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.0b

regimes128.0ms

Accuracy

0% (0.5b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	27
1	33	27
2	33	27
done	33	27

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	1948×	body	1280	valid
674.0ms	7994×	body	80	valid
584.0ms	1525×	body	640	valid
188.0ms	706×	body	320	valid
46.0ms	252×	body	160	valid