Details

sample419.0ms

Algorithm

intervals

Results

47.0ms	260×	body	80	valid
40.0ms	59×	body	1280	valid
20.0ms	45×	body	640	valid
7.0ms	20×	body	320	valid
2.0ms	11×	body	160	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune17.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.4b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.re)
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite30.0ms

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:

4.0ms	(* (atan2 x.im x.re) y.re)
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
148.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify73.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	189	422
1	491	385
2	1112	381
3	2385	381
4	5001	381

prune290.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Merged error: 19.0b

Counts

70 → 5

localize16.0ms

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)
1.7b	(* (atan2 x.im x.re) y.im)
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

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:

4.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
91.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	280	545
1	825	486
2	2165	481
3	5001	481

prune256.0ms

Filtered

81 candidates to 60 candidates (74.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	78	8	86

Merged error: 3.6b

Counts

86 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

5.9b	(cbrt (atan2 x.im x.re))
5.9b	(cbrt (atan2 x.im x.re))
5.9b	(cbrt (atan2 x.im x.re))
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(cbrt (atan2 x.im x.re))
40.0ms	(cbrt (atan2 x.im x.re))
43.0ms	(cbrt (atan2 x.im x.re))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	108	262
1	262	244
2	624	238
3	1701	238
4	5001	238

prune229.0ms

Filtered

60 candidates to 46 candidates (76.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	59	9	68

Merged error: 3.6b

Counts

68 → 9

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp (neg (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
0.0b	(exp (neg (* (atan2 x.im x.re) y.im)))
1.7b	(* (atan2 x.im x.re) y.im)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

87×	`times-frac`
58×	`add-sqr-sqrt`
56×	`add-cube-cbrt` `*-un-lft-identity`
52×	`unpow-prod-down`
17×	`associate-/r*`
9×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`exp-prod`
5×	`pow1` `div-exp` `div-inv` `add-log-exp`
4×	`sqr-pow`
3×	`associate-r` `associate-l` `associate-/l*`
2×	`neg-sub0` `exp-neg` `exp-diff` `pow-exp` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `distribute-lft-neg-in` `pow-to-exp` `neg-mul-1` `distribute-rgt-neg-in` `frac-2neg` `pow-prod-down` `neg-log` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 123

Calls

3 calls:

9.0ms	(/ (exp (neg (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
2.0ms	(exp (neg (* (atan2 x.im x.re) y.im)))
4.0ms	(* (atan2 x.im x.re) y.im)

series132.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(/ (exp (neg (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
23.0ms	(exp (neg (* (atan2 x.im x.re) y.im)))
16.0ms	(* (atan2 x.im x.re) y.im)

simplify56.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	467	1459
1	1753	1412
2	5001	1410

prune375.0ms

Filtered

132 candidates to 101 candidates (76.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	132	9	141

Merged error: 3.6b

Counts

141 → 9

Details

sample419.0ms

simplify39.0ms

prune17.0ms

localize24.0ms

rewrite30.0ms

series238.0ms

simplify73.0ms

prune290.0ms

localize16.0ms

rewrite19.0ms

series238.0ms

simplify62.0ms

prune256.0ms

localize23.0ms

rewrite8.0ms

series161.0ms

simplify60.0ms

prune229.0ms

localize12.0ms

rewrite21.0ms

series132.0ms

simplify56.0ms

prune375.0ms

regimes307.0ms

bsearch5.0ms

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