Details

sample303.0ms

Algorithm

intervals

Results

118.0ms	67×	body	1280	valid
39.0ms	247×	body	80	valid
35.0ms	52×	body	640	valid
14.0ms	28×	body	320	valid
3.0ms	9×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1130
4	249
3	99
2	63
1	35
0	19

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
1.8b	(* (atan2 x.im x.re) y.re)
3.7b	(pow (exp y.im) (atan2 x.im x.re))
32.9b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

343×	`times-frac`
175×	`add-sqr-sqrt`
173×	`*-un-lft-identity` `add-cube-cbrt`
153×	`unpow-prod-down`
51×	`sqr-pow`
29×	`add-exp-log`
25×	`associate-/r*`
21×	`div-exp`
11×	`add-cbrt-cube`
9×	`div-inv`
8×	`pow-to-exp` `pow-exp`
7×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `exp-prod` `associate-r` `associate-l`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 286

Calls

4 calls:

17.0ms	(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
15.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(pow (exp y.im) (atan2 x.im x.re))
7.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series702.0ms

Counts

4 → 12

Calls

4 calls:

430.0ms	(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
27.0ms	(* (atan2 x.im x.re) y.re)
44.0ms	(pow (exp y.im) (atan2 x.im x.re))
199.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify833.0ms

Counts

298 → 298

Iterations

Iter	Nodes
done	5000
1	1415
0	529

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (pow (hypot x.re x.im) y.re) (* (exp (- (* (atan2 x.im x.re) y.im))) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
1.8b	(* (atan2 x.im x.re) y.re)
2.6b	(* (atan2 x.im x.re) y.im)
32.9b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `associate-l`
11×	`prod-exp`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
7×	`associate-r`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `*-commutative`
2×	`pow-to-exp` `pow-prod-down` `associate-l/` `pow-exp` `associate-r/` `unswap-sqr`
1×	`neg-sub0` `exp-neg` `cos-sum` `exp-diff` `fma-udef` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

69.0ms	(* (pow (hypot x.re x.im) y.re) (* (exp (- (* (atan2 x.im x.re) y.im))) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
10.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series733.0ms

Counts

4 → 12

Calls

4 calls:

496.0ms	(* (pow (hypot x.re x.im) y.re) (* (exp (- (* (atan2 x.im x.re) y.im))) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
24.0ms	(* (atan2 x.im x.re) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
193.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1790
1	400
0	169

prune846.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

localize52.0ms

Local error

Found 4 expressions with local error:

6.5b	(cbrt (* (atan2 x.im x.re) y.im))
6.5b	(cbrt (* (atan2 x.im x.re) y.im))
6.5b	(cbrt (* (atan2 x.im x.re) y.im))
32.9b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 43

Calls

4 calls:

3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (* (atan2 x.im x.re) y.im))
112.0ms	(cbrt (* (atan2 x.im x.re) y.im))
106.0ms	(cbrt (* (atan2 x.im x.re) y.im))
167.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify806.0ms

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
3	1397
2	360
1	149
0	81

prune726.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize66.0ms

Local error

Found 4 expressions with local error:

6.5b	(cbrt (* (atan2 x.im x.re) y.im))
6.5b	(cbrt (* (atan2 x.im x.re) y.im))
6.5b	(cbrt (* (atan2 x.im x.re) y.im))
32.9b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 43

Calls

4 calls:

5.0ms	(cbrt (* (atan2 x.im x.re) y.im))
5.0ms	(cbrt (* (atan2 x.im x.re) y.im))
6.0ms	(cbrt (* (atan2 x.im x.re) y.im))
5.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series543.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (* (atan2 x.im x.re) y.im))
116.0ms	(cbrt (* (atan2 x.im x.re) y.im))
115.0ms	(cbrt (* (atan2 x.im x.re) y.im))
219.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify925.0ms

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
3	1397
2	360
1	149
0	81

prune716.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.6b

regimes560.0ms

Accuracy

33.3% (3.2b remaining)

Error of 7.2b against oracle of 3.9b and baseline of 8.8b

bsearch1.2s

Steps

Iters	Range		Point
7	2.5342496629954813e+96	2.0241933620136535e+98	2.9930584338676547e+97
11	5.153441359626629e+30	3.022044278244183e+53	1.3042654153127709e+38
7	-1.5302910996514267e+164	-9.135146609706683e+162	-3.05499739068864e+163

simplify8.0ms

Iterations

Iter	Nodes
done	63
2	63
1	59
0	48

end0.0ms

sample8.0s

Algorithm

intervals

Results

3.2s	2027×	body	1280	valid
1.6s	7967×	body	80	valid
1.3s	1404×	body	640	valid
959.0ms	647×	body	320	valid
106.0ms	299×	body	160	valid