Details

sample4.7s

Algorithm

intervals

Results

4.4s	934×	body	10240	exit
118.0ms	256×	body	80	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
6	6248
5	982
4	286
3	142
2	97
1	69
0	19

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (atan2 x.im x.re) y.im)
23.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
27.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
4×	`sqrt-div` `insert-posit16` `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 → 60

Calls

4 calls:

11.0ms	(* (atan2 x.im x.re) y.im)
31.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 x.im x.re) y.im)
193.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
84.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.4s

Counts

72 → 72

Iterations

Iter	Nodes
5	4446
4	1994
3	1152
2	671
1	385
0	99

prune1.3s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.0b

localize51.0ms

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	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.3b	(* (atan2 x.im x.re) y.im)
27.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite61.0ms

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:

11.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
19.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
135.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
29.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify831.0ms

Counts

82 → 82

Iterations

Iter	Nodes
3	2361
2	1108
1	549
0	135

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

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:

7.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
6.0ms	(* (log (- x.re)) y.re)
10.0ms	(* (atan2 x.im x.re) y.im)

series307.0ms

Counts

3 → 9

Calls

3 calls:

165.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
124.0ms	(* (log (- x.re)) y.re)
18.0ms	(* (atan2 x.im x.re) y.im)

simplify1.8s

Counts

61 → 61

Iterations

Iter	Nodes
4	3665
3	1816
2	852
1	428
0	107

prune856.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize45.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* y.re (log x.im)) (* y.im (atan2 x.im x.re)))
0.1b	(* y.re (log x.im))
0.3b	(* y.im (atan2 x.im x.re))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`log-prod`
11×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
7×	`add-cbrt-cube` `associate-r` `add-exp-log`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `associate--l+`
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 → 64

Calls

3 calls:

8.0ms	(- (* y.re (log x.im)) (* y.im (atan2 x.im x.re)))
7.0ms	(* y.re (log x.im))
6.0ms	(* y.im (atan2 x.im x.re))

series211.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(- (* y.re (log x.im)) (* y.im (atan2 x.im x.re)))
74.0ms	(* y.re (log x.im))
21.0ms	(* y.im (atan2 x.im x.re))

simplify1.5s

Counts

73 → 73

Iterations

Iter	Nodes
4	3412
3	1442
2	750
1	451
0	120

prune1.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes282.0ms

Accuracy

98% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 7.0b

bsearch1.9s

Steps

Iters	Range		Point
7	-2698469.12756182	-31142.171529168027	-31550.873164050485

simplify5.0ms

Iterations

Iter	Nodes
2	33
1	33
0	25

end0.0ms

sample2.0m

Algorithm

intervals

Results

2.0m	29517×	body	10240	exit
3.3s	8000×	body	80	valid