Details

sample4.8s

Algorithm

intervals

Results

4.5s	1047×	body	10240	exit
117.0ms	256×	body	80	valid

simplify3.8s

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: 31.6b

localize74.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (atan2 x.im x.re) y.re)
24.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite54.0ms

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:

6.0ms	(* (atan2 x.im x.re) y.re)
22.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (atan2 x.im x.re) y.re)
209.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.0s

Counts

72 → 72

Iterations

Iter	Nodes
5	4233
4	1689
3	826
2	412
1	198
0	97

prune1.3s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize48.0ms

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)
0.3b	(* (atan2 x.im x.re) y.im)
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite48.0ms

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:

8.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
15.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
11.0ms	(* (atan2 x.im x.re) y.im)
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
115.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
22.0ms	(* (atan2 x.im x.re) y.im)
54.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.5s

Counts

82 → 82

Iterations

Iter	Nodes
4	4236
3	1847
2	751
1	307
0	135

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.2b	(* (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:

8.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
11.0ms	(* (log (- x.re)) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)

series259.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
105.0ms	(* (log (- x.re)) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)

simplify1.8s

Counts

61 → 61

Iterations

Iter	Nodes
4	3360
3	1467
2	585
1	237
0	107

prune814.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`log-prod`
15×	`*-un-lft-identity` `add-cube-cbrt`
12×	`associate--l+`
9×	`distribute-rgt-in` `pow1` `distribute-lft-in` `add-log-exp`
8×	`add-cbrt-cube` `exp-sum` `add-exp-log`
7×	`associate-r`
6×	`associate-l`
4×	`insert-posit16`
3×	`exp-prod`
2×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`
1×	`flip3--` `exp-diff` `log-pow` `flip--`

Counts

4 → 86

Calls

4 calls:

31.0ms	(exp (- (* y.re (log x.im)) (* (atan2 x.im x.re) y.im)))
16.0ms	(- (* y.re (log x.im)) (* (atan2 x.im x.re) y.im))
13.0ms	(* y.re (log x.im))
10.0ms	(* (atan2 x.im x.re) y.im)

series239.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(exp (- (* y.re (log x.im)) (* (atan2 x.im x.re) y.im)))
115.0ms	(- (* y.re (log x.im)) (* (atan2 x.im x.re) y.im))
40.0ms	(* y.re (log x.im))
18.0ms	(* (atan2 x.im x.re) y.im)

simplify3.2s

Counts

98 → 98

Iterations

Iter	Nodes
4	5657
3	1926
2	672
1	313
0	149

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes246.0ms

Accuracy

97.9% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 6.8b

bsearch2.0s

Steps

Iters	Range		Point
7	-2.868526113108925e-11	-1.5917908160649244e-13	-2.8254894938573524e-11

simplify8.0ms

Iterations

Iter	Nodes
2	33
1	33
0	25

end0.0ms

sample2.2m

Algorithm

intervals

Results

2.1m	30970×	body	10240	exit
2.9s	8000×	body	80	valid