Details

sample342.0ms

Algorithm

intervals

Results

216.0ms	260×	body	80	valid
58.0ms	78×	body	1280	valid
21.0ms	42×	body	640	valid
9.0ms	26×	body	320	valid
4.0ms	2×	body	2560	valid
2.0ms	9×	body	160	valid

simplify407.0ms

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

prune15.0ms

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: 34.4b

Counts

2 → 1

localize45.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.re)
30.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

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

series91.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.re)
63.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify76.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	204	434
1	529	395
2	1179	392
3	2603	392
4	5002	392

prune145.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	9	69

Merged error: 20.9b

Counts

69 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

30.0b	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.8b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
31.8b	(cbrt (+ (* x.re x.re) (* x.im x.im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

10.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	263	650
1	721	594
2	2172	582
3	5002	565

prune155.0ms

Filtered

56 candidates to 61 candidates (-8.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	61	9	70

Merged error: 20.9b

Counts

70 → 9

localize36.0ms

Local error

Found 4 expressions with local error:

29.9b	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.8b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
31.8b	(cbrt (+ (* x.re x.re) (* x.im x.im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

13.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (exp (log (cbrt (+ (* x.re x.re) (* x.im x.im)))))))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
24.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	265	674
1	725	614
2	2192	602
3	5002	585

prune152.0ms

Filtered

55 candidates to 61 candidates (-10.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	61	9	70

Merged error: 20.9b

Counts

70 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series23.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify142.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 5 (134.0ms)

Iter	Nodes	Cost
0	89	400
1	215	388
2	503	388
3	1265	388
4	4227	388
5	5002	384

prune96.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	73	8	81

Merged error: 20.9b

Counts

81 → 8

regimes418.0ms

Accuracy

77.2% (3.1b remaining)

Error of 22.6b against oracle of 19.5b and baseline of 33.1b

bsearch122.0ms

Steps

Iters	Range		Point
10	-3.069211600425411e-302	4.251265814292649e-304	1.5656916858478e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	39
1	50	39

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	2191×	body	1280	valid
871.0ms	7935×	body	80	valid
712.0ms	1442×	body	640	valid
188.0ms	550×	body	320	valid
77.0ms	47×	body	2560	valid
51.0ms	228×	body	160	valid

Details

sample342.0ms

simplify407.0ms

prune15.0ms

localize45.0ms

rewrite22.0ms

series91.0ms

simplify76.0ms

prune145.0ms

localize32.0ms

rewrite21.0ms

series180.0ms

simplify62.0ms

prune155.0ms

localize36.0ms

rewrite25.0ms

series181.0ms

simplify63.0ms

prune152.0ms

localize28.0ms

rewrite17.0ms

series23.0ms

simplify142.0ms

prune96.0ms

regimes418.0ms

bsearch122.0ms

simplify2.0ms

end0.0ms

sample4.1s

Profiling