Details

sample248.0ms

Algorithm

intervals

Results

86.0ms	69×	body	1280	valid
29.0ms	252×	body	80	valid
23.0ms	45×	body	640	valid
6.0ms	16×	body	320	valid
2.0ms	7×	body	160	valid

simplify440.0ms

Counts: 1 → 1

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.1b

localize81.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
30.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `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 → 56

Calls

4 calls:

8.0ms	(* (atan2 x.im x.re) y.im)
33.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (atan2 x.im x.re) y.im)
224.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
77.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.2s

Counts: 68 → 68

prune551.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (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)
1.7b	(* (atan2 x.im x.re) y.im)
31.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

44.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
22.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
150.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
35.0ms	(* (atan2 x.im x.re) y.im)
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify940.0ms

Counts: 81 → 81

prune478.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
0.1b	(* (log x.re) y.re)
1.7b	(* (atan2 x.im x.re) y.im)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

26.0ms	(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
17.0ms	(* (log x.re) y.re)
15.0ms	(* (atan2 x.im x.re) y.im)

series308.0ms

Counts

3 → 9

Calls

3 calls:

185.0ms	(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
87.0ms	(* (log x.re) y.re)
35.0ms	(* (atan2 x.im x.re) y.im)

simplify1.3s

Counts: 58 → 58

prune227.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.8b

localize83.0ms

Local error

Found 4 expressions with local error:

31.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
63.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
47.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
73.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.4s

Counts: 72 → 72

prune744.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.7b

regimes424.0ms

Accuracy

68.7% (5.1b remaining)

Error of 8.5b against oracle of 3.4b and baseline of 19.8b

bsearch205.0ms

Steps

Iters	Range		Point
9	-3.077765773438951e-304	1.66707864824975e-307	2.69463732598623e-310

simplify995.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

2.8s	2018×	body	1280	valid
2.7s	8047×	body	80	valid
1.2s	1415×	body	640	valid
472.0ms	644×	body	320	valid
110.0ms	339×	body	160	valid