Details

sample308.0ms

Algorithm

intervals

Results

123.0ms	62×	body	1280	valid
43.0ms	259×	body	80	valid
28.0ms	43×	body	640	valid
9.0ms	23×	body	320	valid
4.0ms	16×	body	160	valid

simplify48.0ms

Counts: 1 → 1

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize56.0ms

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)))
34.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite54.0ms

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)
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
23.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (atan2 x.im x.re) y.im)
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
268.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify64.0ms

Counts: 68 → 68

prune541.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.3b

localize38.0ms

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)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.3b	(* (atan2 x.im x.re) y.im)
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite97.0ms

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:

30.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
34.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
14.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
140.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify72.0ms

Counts: 81 → 81

prune435.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.0b	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
0.1b	(* (log (* -1 x.re)) y.re)
2.3b	(* (atan2 x.im x.re) y.im)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

11.0ms	(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
52.0ms	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
19.0ms	(* (log (* -1 x.re)) y.re)
15.0ms	(* (atan2 x.im x.re) y.im)

series390.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
92.0ms	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
126.0ms	(* (log (* -1 x.re)) y.re)
31.0ms	(* (atan2 x.im x.re) y.im)

simplify141.0ms

Counts: 77 → 77

prune306.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.6b

localize45.0ms

Local error

Found 4 expressions with local error:

6.0b	(cbrt (atan2 x.im x.re))
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(cbrt (atan2 x.im x.re))
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
234.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

Counts: 61 → 61

prune433.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.6b

regimes433.0ms

bsearch1.4s

Steps

Iters	Range		Point
9	1.3196812780970065e-63	7.858103861298114e-57	9.566811640023863e-61
8	1.3242107209789743e-236	1.1621273763107636e-232	3.79042976669168e-233
10	-1.9739641733344554e-305	8.845804037490812e-301	-1.59374399213355e-310
9	-1.4140900430281582e-101	-5.0983811848635975e-111	-1.5553813579428227e-106
8	-9.293159657633626e-75	-5.204170981472124e-78	-1.0705897642595153e-75

Details

sample308.0ms

simplify48.0ms

prune22.0ms

localize56.0ms

rewrite54.0ms

series384.0ms

simplify64.0ms

prune541.0ms

localize38.0ms

rewrite97.0ms

series358.0ms

simplify72.0ms

prune435.0ms

localize31.0ms

rewrite99.0ms

series390.0ms

simplify141.0ms

prune306.0ms

localize45.0ms

rewrite53.0ms

series386.0ms

simplify78.0ms

prune433.0ms

regimes433.0ms

bsearch1.4s

simplify86.0ms