Details

sample450.0ms

Algorithm

intervals

Results

125.0ms	261×	body	80	valid
107.0ms	50×	body	1280	valid
51.0ms	44×	body	640	valid
16.0ms	23×	body	320	valid
6.0ms	2×	body	2560	valid
4.0ms	10×	body	160	valid

simplify789.0ms

Counts: 1 → 1

prune70.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.6b

localize121.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (atan2 x.im x.re) y.re)
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite56.0ms

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:

8.0ms	(* (atan2 x.im x.re) y.re)
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (atan2 x.im x.re) y.re)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
189.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts: 68 → 68

prune620.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.3b

localize62.0ms

Local error

Found 4 expressions with local error:

29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
225.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
75.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
266.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts: 65 → 65

prune676.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 17.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

122.0ms	(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
19.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series470.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
59.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
292.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify1.4s

Counts: 74 → 74

prune525.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.2b

localize91.0ms

Local error

Found 4 expressions with local error:

29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
30.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
44.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series838.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
258.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
254.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
263.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify2.8s

Counts: 51 → 51

prune590.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 17.2b

regimes634.0ms

Accuracy

76% (3.3b remaining)

Error of 22.4b against oracle of 19.1b and baseline of 32.9b

bsearch187.0ms

Steps

Iters	Range		Point
9	-4.189320577074054e-303	3.0425610743120056e-307	-3.2986437820904e-310

simplify1.0s

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.0s	2139×	body	1280	valid
2.3s	1425×	body	640	valid
2.2s	8002×	body	80	valid
343.0ms	582×	body	320	valid
127.0ms	52×	body	2560	valid
83.0ms	227×	body	160	valid