Details

analyze1.5s

Algorithm: search

sample138.0ms

Algorithm

intervals

Results

50.0ms	65×	body	1280	invalid
29.0ms	245×	body	80	valid
16.0ms	31×	body	640	invalid
7.0ms	18×	body	320	invalid
3.0ms	3×	body	1280	valid
3.0ms	2×	body	2560	invalid
2.0ms	5×	body	320	valid
1.0ms	3×	body	640	valid
1.0ms	12×	body	80	invalid
1.0ms	5×	body	160	invalid

simplify382.0ms

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

prune28.0ms

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: 36.3b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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×	`sin-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)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series93.0ms

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)))
74.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify81.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	206	434
1	539	395
2	1201	392
3	2732	392
4	5002	392

prune119.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	63	6	69

Merged error: 18.9b

Counts

69 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series177.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
58.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
56.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify62.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (55.0ms)

Iter	Nodes	Cost
0	152	580
1	321	508
2	672	505
3	1724	505
4	5001	504

prune105.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	50	7	57

Merged error: 18.9b

Counts

57 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.re)
2.2b	(* (atan2 x.im x.re) y.im)
20.6b	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `flip-+`

Counts

4 → 59

Calls

4 calls:

4.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify102.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	260	372
1	715	332
2	1646	328
3	3711	328
4	5001	328

prune143.0ms

Filtered

51 candidates to 71 candidates (-39.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	69	9	78

Merged error: 9.8b

Counts

78 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (log (* -1 x.re)) y.im)
1.6b	(* (atan2 x.im x.re) y.re)
2.2b	(* (atan2 x.im x.re) y.im)
20.6b	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`pow1`
11×	`associate-l`
10×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r`
4×	`pow-prod-down` `add-log-exp`
3×	`prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`log-pow`
1×	`sin-sum`

Counts

4 → 64

Calls

4 calls:

7.0ms	(* (log (* -1 x.re)) y.im)
3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (log (* -1 x.re)) y.im)
6.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sin (+ (* (log (* -1 x.re)) y.im) (* (atan2 x.im x.re) y.re)))

simplify57.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	241	378
1	763	324
2	2947	323
3	5002	323

prune124.0ms

Filtered

50 candidates to 76 candidates (-52.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	73	12	85

Merged error: 9.8b

Counts

85 → 12

regimes686.0ms

Accuracy

80.6% (5.0b remaining)

Error of 17.9b against oracle of 12.9b and baseline of 38.4b

bsearch5.8s

Steps

Iters	Range		Point
10	-3.926776353740267e-303	1.785518082097725e-303	2.7089950258453e-310
8	-5.963388787632845e-233	-1.2485833258272383e-236	-1.1804736302167094e-234
11	-6.349566770326335e-121	-1.4247917558707154e-142	-1.4391871695144185e-142
10	-5.242171997896957e+33	-8.95678556777923e+19	-9.121782091145393e+19

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	93
1	66	93

end0.0ms

analyze1.2s

Algorithm: search

sample4.0s

Algorithm

intervals

Results

1.5s	2074×	body	1280	invalid
854.0ms	7546×	body	80	valid
645.0ms	1264×	body	640	invalid
167.0ms	472×	body	320	invalid
99.0ms	126×	body	1280	valid
85.0ms	174×	body	640	valid
80.0ms	49×	body	2560	invalid
45.0ms	187×	body	160	invalid
45.0ms	361×	body	80	invalid
37.0ms	106×	body	320	valid
12.0ms	48×	body	160	valid

Details

analyze1.5s

sample138.0ms

simplify382.0ms

prune28.0ms

localize24.0ms

rewrite21.0ms

series93.0ms

simplify81.0ms

prune119.0ms

localize26.0ms

rewrite25.0ms

series177.0ms

simplify62.0ms

prune105.0ms

localize26.0ms

rewrite18.0ms

series58.0ms

simplify102.0ms

prune143.0ms

localize17.0ms

rewrite21.0ms

series63.0ms

simplify57.0ms

prune124.0ms

regimes686.0ms

bsearch5.8s

simplify2.0ms

end0.0ms

analyze1.2s

sample4.0s

Profiling