Details

sample351.0ms

Algorithm

intervals

Results

150.0ms	79×	body	1280	valid
46.0ms	251×	body	80	valid
32.0ms	39×	body	640	valid
8.0ms	12×	body	320	valid
3.0ms	7×	body	160	valid
2.0ms	1×	body	2560	valid

simplify520.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize65.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
31.0b	(sin (+ (* (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)))

rewrite97.0ms

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

Counts

4 → 56

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sin (+ (* (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)))
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (atan2 x.im x.re) y.im)
240.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
69.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.3s

Counts: 68 → 68

prune493.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.1b

localize74.0ms

Local error

Found 4 expressions with local error:

7.4b	(cbrt (* (atan2 x.im x.re) y.im))
31.0b	(sin (+ (* (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)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cbrt-prod` `sin-sum` `pow1/3`

Counts

4 → 47

Calls

4 calls:

3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
18.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (* (atan2 x.im x.re) y.im))
213.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
61.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.1s

Counts: 59 → 59

prune478.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.1b

localize73.0ms

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)))

rewrite49.0ms

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:

8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.4s

Counts: 72 → 72

prune857.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.1b

localize51.0ms

Local error

Found 4 expressions with local error:

12.2b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
31.0b	(sin (+ (* (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)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `cube-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cube-mult` `sin-sum` `pow1/3` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 59

Calls

4 calls:

12.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
24.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
206.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.7s

Counts: 71 → 71

prune652.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.1b

regimes681.0ms

Accuracy

77.4% (3.2b remaining)

Error of 22.7b against oracle of 19.5b and baseline of 33.6b

bsearch260.0ms

Steps

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

simplify742.0ms

end0.0ms

sample9.4s

Algorithm

intervals

Results

2.9s	8019×	body	80	valid
2.9s	2210×	body	1280	valid
2.0s	1364×	body	640	valid
368.0ms	562×	body	320	valid
202.0ms	261×	body	160	valid
118.0ms	47×	body	2560	valid