Details

sample7.3s

Algorithm

intervals

Results

7.0s	1543×	body	10240	exit
172.0ms	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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (atan2 x.im x.re) y.re)
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite45.0ms

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×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

5.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (atan2 x.im x.re) y.re)
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
204.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

72 → 72

Iterations

Iter	Nodes
5	4148
4	1674
3	836
2	412
1	203
0	100

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.5b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (- x.re)) y.im)
0.3b	(* (atan2 x.im x.re) y.re)
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.2b	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

14.0ms	(* (log (- x.re)) y.im)
10.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (log (- x.re)) y.im)
29.0ms	(* (atan2 x.im x.re) y.re)
48.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
229.0ms	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

76 → 76

Iterations

Iter	Nodes
4	4359
3	1334
2	603
1	285
0	138

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.9b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (- x.re)) y.re)
0.3b	(* (log (- x.re)) y.im)
0.3b	(* (atan2 x.im x.re) y.re)
37.2b	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`pow1`
11×	`associate-l`
10×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`log-pow`
1×	`sin-sum`

Counts

4 → 68

Calls

4 calls:

7.0ms	(* (log (- x.re)) y.re)
13.0ms	(* (log (- x.re)) y.im)
8.0ms	(* (atan2 x.im x.re) y.re)
20.0ms	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (log (- x.re)) y.re)
84.0ms	(* (log (- x.re)) y.im)
26.0ms	(* (atan2 x.im x.re) y.re)
199.0ms	(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

80 → 80

Iterations

Iter	Nodes
5	2866
4	1684
3	1036
2	556
1	252
0	123

prune1.4s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 4.9b

localize67.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (log (- x.re)))
0.6b	(cbrt (log (- x.re)))
0.6b	(cbrt (log (- x.re)))
37.2b	(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
7×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3` `log-pow`
1×	`sin-sum`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt (log (- x.re)))
1.0ms	(cbrt (log (- x.re)))
1.0ms	(cbrt (log (- x.re)))
86.0ms	(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))

series1.7s

Counts

4 → 12

Calls

4 calls:

489.0ms	(cbrt (log (- x.re)))
473.0ms	(cbrt (log (- x.re)))
507.0ms	(cbrt (log (- x.re)))
199.0ms	(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))

simplify2.9s

Counts

60 → 60

Iterations

Iter	Nodes
7	5157
6	1835
5	793
4	392
3	244
2	165
1	111
0	65

prune1.1s

Pruning

17 alts after pruning (13 fresh and 4 done)

Merged error: 4.9b

regimes1.2s

Accuracy

44.4% (6.2b remaining)

Error of 11.3b against oracle of 5.1b and baseline of 16.2b

bsearch4.1s

Steps

Iters	Range		Point
7	-1.6137894966391705e-239	-1.3889369789878345e-241	-1.280939127235916e-239
7	-7.086233488937718e-226	-7.087302104501789e-228	-4.83786766224259e-227
6	-17732119.21706773	-1607553.2698906797	-1694155.0241369938

simplify13.0ms

Iterations

Iter	Nodes
2	53
1	53
0	38

end0.0ms

sample3.4m

Algorithm

intervals

Results

3.3m	47126×	body	10240	exit
4.0s	8000×	body	80	valid