Details

analyze1.5s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

sample137.0ms

Algorithm

intervals

Results

46.0ms	55×	body	1280	invalid
27.0ms	237×	body	80	valid
22.0ms	43×	body	640	invalid
6.0ms	17×	body	320	invalid
3.0ms	9×	body	320	valid
3.0ms	4×	body	1280	valid
3.0ms	12×	body	160	invalid
2.0ms	4×	body	640	valid
2.0ms	18×	body	80	invalid
1.0ms	2×	body	160	valid

simplify516.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4970	36
1	4970	36

prune20.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 35.4b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.im)
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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

series88.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
70.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify56.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4737	680
1	4737	680

prune146.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 21.4b

Counts

70 → 7

localize17.0ms

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)
1.9b	(* (atan2 x.im x.re) y.im)
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite17.0ms

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` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `exp-sum` `flip-+`

Counts

4 → 68

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)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
23.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify29.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5242	850

prune151.0ms

Filtered

61 candidates to 80 candidates (-31.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	76	11	87

Merged error: 4.8b

Counts

87 → 11

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (exp (atan2 x.im x.re)) (neg y.im)) (pow (/ -1 x.re) y.re))
0.4b	(exp (atan2 x.im x.re))
0.4b	(pow (exp (atan2 x.im x.re)) (neg y.im))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

191×	`times-frac`
161×	`unpow-prod-down`
109×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`sqr-pow`
19×	`add-exp-log`
17×	`associate-/r*`
15×	`div-exp`
11×	`pow-exp`
10×	`pow-unpow`
9×	`div-inv`
8×	`pow-to-exp`
7×	`associate-/l*`
6×	`exp-prod`
5×	`add-cbrt-cube`
4×	`pow1` `pow-pow` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`neg-sub0` `pow-neg` `associate-/l/` `pow-sub`
1×	`cbrt-undiv` `neg-mul-1` `frac-2neg` `clear-num` `rem-exp-log`

Counts

3 → 208

Calls

3 calls:

10.0ms	(/ (pow (exp (atan2 x.im x.re)) (neg y.im)) (pow (/ -1 x.re) y.re))
2.0ms	(exp (atan2 x.im x.re))
4.0ms	(pow (exp (atan2 x.im x.re)) (neg y.im))

series49.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(/ (pow (exp (atan2 x.im x.re)) (neg y.im)) (pow (/ -1 x.re) y.re))
4.0ms	(exp (atan2 x.im x.re))
13.0ms	(pow (exp (atan2 x.im x.re)) (neg y.im))

simplify67.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5008	4722

prune372.0ms

Filtered

155 candidates to 217 candidates (-40.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	217	11	228

Merged error: 4.8b

Counts

228 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 x.im x.re))
0.4b	(exp (atan2 x.im x.re))
0.4b	(pow (exp (atan2 x.im x.re)) (neg y.im))
0.4b	(pow (exp (atan2 x.im x.re)) (neg y.im))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow-unpow`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`exp-prod`
8×	`pow-pow`
6×	`pow1` `distribute-lft-neg-in` `unpow-prod-down` `distribute-rgt-neg-in` `add-log-exp`
4×	`add-exp-log` `add-cbrt-cube`
2×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-exp` `rem-exp-log` `pow-sub` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

2.0ms	(exp (atan2 x.im x.re))
2.0ms	(exp (atan2 x.im x.re))
4.0ms	(pow (exp (atan2 x.im x.re)) (neg y.im))
4.0ms	(pow (exp (atan2 x.im x.re)) (neg y.im))

series34.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(exp (atan2 x.im x.re))
4.0ms	(exp (atan2 x.im x.re))
13.0ms	(pow (exp (atan2 x.im x.re)) (neg y.im))
13.0ms	(pow (exp (atan2 x.im x.re)) (neg y.im))

simplify74.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4864	690
1	4864	690

prune143.0ms

Filtered

58 candidates to 92 candidates (-58.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	92	11	103

Merged error: 4.8b

Counts

103 → 11

regimes552.0ms

Accuracy

57.6% (6.9b remaining)

Error of 10.7b against oracle of 3.7b and baseline of 20.0b

bsearch2.7s

Steps

Iters	Range		Point
8	7.178061669870633e-57	4.258499589527743e-52	1.4668072428131629e-52
9	-2.3335637489488046e-307	9.826630474863851e-305	-3.8865966887532446e-308

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	48
1	41	48

end0.0ms

analyze1.3s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

sample3.7s

Algorithm

intervals

Results

1.3s	1877×	body	1280	invalid
854.0ms	7550×	body	80	valid
634.0ms	1298×	body	640	invalid
192.0ms	552×	body	320	invalid
104.0ms	138×	body	1280	valid
66.0ms	135×	body	640	valid
58.0ms	256×	body	160	invalid
48.0ms	127×	body	320	valid
45.0ms	390×	body	80	invalid
12.0ms	50×	body	160	valid

Details

analyze1.5s

sample137.0ms

simplify516.0ms

prune20.0ms

localize26.0ms

rewrite22.0ms

series88.0ms

simplify56.0ms

prune146.0ms

localize17.0ms

rewrite17.0ms

series75.0ms

simplify29.0ms

prune151.0ms

localize15.0ms

rewrite29.0ms

series49.0ms

simplify67.0ms

prune372.0ms

localize20.0ms

rewrite14.0ms

series34.0ms

simplify74.0ms

prune143.0ms

regimes552.0ms

bsearch2.7s

simplify2.0ms

end0.0ms

analyze1.3s

sample3.7s

Profiling