Details

sample4.0s

Algorithm

intervals

Results

3.8s	972×	body	10240	exit
72.0ms	256×	body	80	valid

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
6	5642
5	808
4	197
3	82
2	53
1	31
0	19

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
26.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

11.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
28.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
222.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
73.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
73.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.3s

Counts

75 → 75

Iterations

Iter	Nodes
5	4347
4	1800
3	914
2	468
1	220
0	106

prune1.5s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize38.0ms

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))
0.3b	(* (atan2 x.im x.re) y.im)
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`pow1`
9×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-r` `add-log-exp`
4×	`insert-posit16`
3×	`log-pow` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

4 → 70

Calls

4 calls:

12.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
10.0ms	(* (atan2 x.im x.re) y.im)
10.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
32.0ms	(* (atan2 x.im x.re) y.im)
107.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
45.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.6s

Counts

82 → 82

Iterations

Iter	Nodes
4	4510
3	1806
2	739
1	307
0	135

prune1.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.3b	(* (atan2 x.im x.re) y.im)
0.3b	(* (log (- x.re)) y.re)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`pow1`
7×	`-un-lft-identity` `add-cbrt-cube` `associate-l*` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
5×	`add-log-exp`
3×	`insert-posit16`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--`

Counts

3 → 52

Calls

3 calls:

16.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
12.0ms	(* (atan2 x.im x.re) y.im)
14.0ms	(* (log (- x.re)) y.re)

series334.0ms

Counts

3 → 9

Calls

3 calls:

190.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
31.0ms	(* (atan2 x.im x.re) y.im)
113.0ms	(* (log (- x.re)) y.re)

simplify1.7s

Counts

61 → 61

Iterations

Iter	Nodes
4	3316
3	1390
2	577
1	237
0	107

prune870.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.1b

regimes236.0ms

Accuracy

98.9% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 7.6b

bsearch2.7s

Steps

Iters	Range		Point
8	-2125.2213841711514	-3.0421098639022524	-3.079284281175841

simplify9.0ms

Iterations

Iter	Nodes
2	33
1	33
0	25

end0.0ms

sample2.1m

Algorithm

intervals

Results

2.0m	30308×	body	10240	exit
2.7s	8000×	body	80	valid