Details

sample385.0ms

Algorithm

intervals

Results

42.0ms	62×	body	1280	valid
26.0ms	253×	body	80	valid
16.0ms	36×	body	640	valid
6.0ms	18×	body	320	valid
4.0ms	2×	body	2560	valid
2.0ms	8×	body	160	valid

simplify42.0ms

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

prune13.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 33.8b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.im)
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(sin (+ (* (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×	`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)))
9.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series251.0ms

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)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
163.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify77.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	196	425
1	506	388
2	1139	386
3	2509	386
4	5001	386

prune322.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	58	10	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	10	69

Merged error: 20.0b

Counts

69 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(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)))

rewrite23.0ms

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:

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)))
11.0ms	(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)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
92.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
90.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
267.0ms	(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)))

simplify68.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	226	599
1	690	543
2	2010	539
3	5002	538

prune412.0ms

Filtered

61 candidates to 56 candidates (91.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	56	5	61
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	61	10	71

Merged error: 19.9b

Counts

71 → 10

localize34.0ms

Local error

Found 4 expressions with local error:

29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(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)))

rewrite28.0ms

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:

6.0ms	(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)))
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)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
95.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
92.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
264.0ms	(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)))

simplify68.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	228	623
1	695	563
2	2039	559
3	5001	558

prune439.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	61	10	71

Merged error: 19.9b

Counts

71 → 10

localize41.0ms

Local error

Found 4 expressions with local error:

29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(sin (+ (* (log (* (fabs (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
32.9b	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow` `sqrt-prod`
2×	`cbrt-div` `flip3-+` `sqrt-div` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow1/3` `sin-sum` `pow1/3` `pow-exp` `sqr-pow`

Counts

4 → 54

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sin (+ (* (log (* (fabs (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)

series496.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
96.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
268.0ms	(sin (+ (* (log (* (fabs (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
95.0ms	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)

simplify103.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	275	590
1	894	515
2	3010	510
3	5001	510

prune389.0ms

Filtered

66 candidates to 57 candidates (86.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	66	10	76

Merged error: 19.9b

Counts

76 → 10

regimes347.0ms

Accuracy

76.6% (3.2b remaining)

Error of 23.2b against oracle of 20.0b and baseline of 33.8b

bsearch139.0ms

Steps

Iters	Range		Point
9	-1.2049654802029013e-301	1.5653172648300943e-307	-5.11927313063325e-309

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	35
1	39	35

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2132×	body	1280	valid
741.0ms	7949×	body	80	valid
613.0ms	1440×	body	640	valid
174.0ms	568×	body	320	valid
66.0ms	43×	body	2560	valid
46.0ms	230×	body	160	valid

Details

sample385.0ms

simplify42.0ms

prune13.0ms

localize25.0ms

rewrite22.0ms

series251.0ms

simplify77.0ms

prune322.0ms

localize31.0ms

rewrite23.0ms

series488.0ms

simplify68.0ms

prune412.0ms

localize34.0ms

rewrite28.0ms

series492.0ms

simplify68.0ms

prune439.0ms

localize41.0ms

rewrite24.0ms

series496.0ms

simplify103.0ms

prune389.0ms

regimes347.0ms

bsearch139.0ms

simplify2.0ms

end0.0ms

sample3.4s

Profiling