Details

sample456.0ms

Algorithm

intervals

Results

146.0ms	67×	body	1280	valid
80.0ms	259×	body	80	valid
66.0ms	41×	body	640	valid
45.0ms	22×	body	320	valid
5.0ms	13×	body	160	valid
2.0ms	1×	body	2560	valid

simplify31.0ms

Counts: 1 → 1

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize108.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (atan2 x.im x.re) y.im)
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite150.0ms

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.im)
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
72.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (atan2 x.im x.re) y.im)
42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
340.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify64.0ms

Counts: 68 → 68

prune643.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.6b

localize66.0ms

Local error

Found 4 expressions with local error:

30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite114.0ms

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:

14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
40.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
39.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series761.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(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)))
235.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
271.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify62.0ms

Counts: 51 → 51

prune556.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 19.6b

localize38.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (atan2 x.im x.re) y.im)
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite100.0ms

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:

14.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (atan2 x.im x.re) y.im)
55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
215.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify83.0ms

Counts: 68 → 68

prune597.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 19.6b

localize58.0ms

Local error

Found 4 expressions with local error:

30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
34.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series630.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
182.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
169.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
217.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify92.0ms

Counts: 61 → 61

prune642.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 19.6b

regimes557.0ms

bsearch198.0ms

Steps

Iters	Range		Point
10	-1.9739641733344554e-305	8.845804037490812e-301	-5.774698178669197e-309

Details

sample456.0ms

simplify31.0ms

prune36.0ms

localize108.0ms

rewrite150.0ms

series471.0ms

simplify64.0ms

prune643.0ms

localize66.0ms

rewrite114.0ms

series761.0ms

simplify62.0ms

prune556.0ms

localize38.0ms

rewrite100.0ms

series338.0ms

simplify83.0ms

prune597.0ms

localize58.0ms

rewrite47.0ms

series630.0ms

simplify92.0ms

prune642.0ms

regimes557.0ms

bsearch198.0ms

simplify36.0ms