Details

sample461.0ms

Algorithm

intervals

Results

62.0ms	62×	body	1280	valid
30.0ms	264×	body	80	valid
16.0ms	33×	body	640	valid
6.0ms	17×	body	320	valid
1.0ms	6×	body	160	valid

simplify37.0ms

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

prune21.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 32.8b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (atan2 x.im x.re) y.im)
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite29.0ms

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:

3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
174.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	191	420
1	501	383
2	1134	381
3	2494	381
4	5002	381

prune422.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 19.0b

Counts

69 → 5

localize21.0ms

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)
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

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)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
111.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
24.0ms	(* (atan2 x.im x.re) y.im)
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	280	546
1	825	487
2	2165	481
3	5001	481

prune498.0ms

Filtered

81 candidates to 60 candidates (25.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	79	7	86

Merged error: 2.3b

Counts

86 → 7

localize13.0ms

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)))
2.3b	(* (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*`
11×	`add-exp-log`
8×	`div-exp`
7×	`add-cbrt-cube`
6×	`exp-prod`
5×	`pow1` `div-inv` `add-log-exp`
4×	`pow-exp` `sqr-pow`
3×	`associate-r` `associate-l` `associate-/l*`
2×	`neg-sub0` `exp-neg` `exp-diff` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `distribute-lft-neg-in` `pow-to-exp` `neg-mul-1` `rec-exp` `distribute-rgt-neg-in` `frac-2neg` `1-exp` `pow-prod-down` `neg-log` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 125

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)))
3.0ms	(* (atan2 x.im x.re) y.im)

series137.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(/ (exp (neg (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
32.0ms	(exp (neg (* (atan2 x.im x.re) y.im)))
19.0ms	(* (atan2 x.im x.re) y.im)

simplify55.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	447	1462
1	1665	1378
2	5002	1369

prune726.0ms

Filtered

134 candidates to 86 candidates (35.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	134	7	141

Merged error: 2.3b

Counts

141 → 7

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
0.2b	(* (log (* -1 x.re)) y.re)
2.3b	(* (atan2 x.im x.re) y.im)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

5.0ms	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms	(* (log (* -1 x.re)) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)

series181.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(exp (- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im)))
81.0ms	(* (log (* -1 x.re)) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)

simplify61.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	214	325
1	697	283
2	2991	278
3	5001	278

prune203.0ms

Filtered

62 candidates to 41 candidates (33.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	61	8	69

Merged error: 2.3b

Counts

69 → 8

regimes548.0ms

Accuracy

56.3% (12.4b remaining)

Error of 15.7b against oracle of 3.4b and baseline of 31.7b

bsearch456.0ms

Steps

Iters	Range	Point
10	-5.561573377002615e-304	3.0877076910478216e-302	4.6617580803001e-311
9	-2.568854389543697e-169	-9.604033086679427e-178	-2.4602008343284792e-169
10	-2.9459745506063908e+143	-4.140015276366134e+133	-3.234651576175647e+138

Iters

Range

Point

-5.561573377002615e-304

3.0877076910478216e-302

4.6617580803001e-311

-2.568854389543697e-169

-9.604033086679427e-178

-2.4602008343284792e-169

-2.9459745506063908e+143

-4.140015276366134e+133

-3.234651576175647e+138

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	50
1	65	50
2	65	50

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.4s	2052×	body	1280	valid
820.0ms	8020×	body	80	valid
663.0ms	1434×	body	640	valid
190.0ms	582×	body	320	valid
67.0ms	310×	body	160	valid

Details

sample461.0ms

simplify37.0ms

prune21.0ms

localize24.0ms

rewrite29.0ms

series295.0ms

simplify76.0ms

prune422.0ms

localize21.0ms

rewrite18.0ms

series290.0ms

simplify58.0ms

prune498.0ms

localize13.0ms

rewrite21.0ms

series137.0ms

simplify55.0ms

prune726.0ms

localize12.0ms

rewrite15.0ms

series181.0ms

simplify61.0ms

prune203.0ms

regimes548.0ms

bsearch456.0ms

simplify3.0ms

end0.0ms

sample3.8s

Profiling