Details

sample398.0ms

Algorithm

intervals

Results

50.0ms	67×	body	1280	valid
35.0ms	50×	body	640	valid
28.0ms	257×	body	80	valid
7.0ms	21×	body	320	valid
2.0ms	10×	body	160	valid

simplify41.0ms

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

prune19.0ms

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: 33.0b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.im)
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.2b	(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)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

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

prune322.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Merged error: 19.6b

Counts

70 → 5

localize18.0ms

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)
1.4b	(* (atan2 x.im x.re) y.im)
29.0b	(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)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
88.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (21.0ms)

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

prune273.0ms

Filtered

81 candidates to 60 candidates (74.1%)

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: 4.1b

Counts

86 → 7

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (neg (* (atan2 x.im x.re) y.im)))
0.3b	(/ (exp (neg (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
1.4b	(* (atan2 x.im x.re) y.im)

rewrite23.0ms

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:

3.0ms	(exp (neg (* (atan2 x.im x.re) y.im)))
10.0ms	(/ (exp (neg (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
6.0ms	(* (atan2 x.im x.re) y.im)

series117.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(exp (neg (* (atan2 x.im x.re) y.im)))
78.0ms	(/ (exp (neg (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
16.0ms	(* (atan2 x.im x.re) y.im)

simplify52.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (38.0ms)

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

prune373.0ms

Filtered

134 candidates to 86 candidates (64.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	133	8	141

Merged error: 4.1b

Counts

141 → 8

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow E (neg (* (atan2 x.im x.re) y.im)))
0.3b	(/ (pow E (neg (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
1.4b	(* (atan2 x.im x.re) y.im)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

191×	`times-frac`
161×	`unpow-prod-down`
109×	`add-sqr-sqrt`
107×	`add-cube-cbrt` `*-un-lft-identity`
42×	`add-exp-log`
32×	`div-exp`
30×	`pow-exp`
27×	`sqr-pow`
17×	`associate-/r*`
11×	`pow-to-exp`
9×	`div-inv`
7×	`e-exp-1` `add-cbrt-cube` `associate-/l*`
6×	`pow1` `pow-unpow`
4×	`rec-exp` `1-exp`
3×	`associate-r` `associate-l` `add-log-exp`
2×	`neg-sub0` `pow-neg` `associate-/l/` `pow-sub`
1×	`cbrt-undiv` `distribute-lft-neg-in` `neg-mul-1` `pow-pow` `distribute-rgt-neg-in` `frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 221

Calls

3 calls:

2.0ms	(pow E (neg (* (atan2 x.im x.re) y.im)))
13.0ms	(/ (pow E (neg (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
4.0ms	(* (atan2 x.im x.re) y.im)

series143.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(pow E (neg (* (atan2 x.im x.re) y.im)))
90.0ms	(/ (pow E (neg (* (atan2 x.im x.re) y.im))) (pow (/ 1 x.re) y.re))
17.0ms	(* (atan2 x.im x.re) y.im)

simplify84.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	629	2870
1	2800	2714
2	5001	2597

prune452.0ms

Filtered

230 candidates to 112 candidates (48.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	230	8	238

Merged error: 4.1b

Counts

238 → 8

regimes361.0ms

Accuracy

80.3% (5.7b remaining)

Error of 9.2b against oracle of 3.5b and baseline of 32.3b

bsearch146.0ms

Steps

Iters	Range		Point
11	-1.329912432178342e-295	2.0275104442738615e-300	-1.5510630416592e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	35	15
2	35	15

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	2043×	body	1280	valid
850.0ms	7955×	body	80	valid
672.0ms	1413×	body	640	valid
222.0ms	657×	body	320	valid
70.0ms	309×	body	160	valid

Details

sample398.0ms

simplify41.0ms

prune19.0ms

localize25.0ms

rewrite22.0ms

series246.0ms

simplify78.0ms

prune322.0ms

localize18.0ms

rewrite19.0ms

series233.0ms

simplify62.0ms

prune273.0ms

localize12.0ms

rewrite23.0ms

series117.0ms

simplify52.0ms

prune373.0ms

localize15.0ms

rewrite31.0ms

series143.0ms

simplify84.0ms

prune452.0ms

regimes361.0ms

bsearch146.0ms

simplify2.0ms

end0.0ms

sample3.6s

Profiling