Details

sample369.0ms

Algorithm

intervals

Results

48.0ms	73×	body	1280	valid
24.0ms	250×	body	80	valid
18.0ms	43×	body	640	valid
5.0ms	16×	body	320	valid
2.0ms	1×	body	2560	valid
1.0ms	4×	body	160	valid

simplify54.0ms

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

prune17.0ms

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: 32.6b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (atan2 x.im x.re) y.im)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

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)))
5.0ms	(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)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
164.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	196	427
1	506	390
2	1139	386
3	2509	386
4	5001	386

prune322.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Merged error: 17.4b

Counts

70 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.4b	(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)))
7.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
146.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
142.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
149.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify165.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (54.0ms)

Iter	Nodes	Cost
0	142	553
1	288	487
2	611	487
3	1523	487
4	4766	486
5	5002	486

prune336.0ms

Filtered

51 candidates to 48 candidates (94.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	51	8	59

Merged error: 17.4b

Counts

59 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.8b	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`cbrt-prod`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cube-mult` `unpow-prod-down` `sin-sum` `pow1/3` `unpow3` `cube-prod` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
2.0ms	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

series249.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
141.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.0ms	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

simplify80.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 4 (74.0ms)

Iter	Nodes	Cost
0	201	447
1	502	417
2	1079	417
3	2495	417
4	5002	415

prune350.0ms

Filtered

67 candidates to 55 candidates (82.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	67	8	75

Merged error: 17.4b

Counts

75 → 8

localize36.0ms

Local error

Found 4 expressions with local error:

29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.8b	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))
35.8b	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
2×	`cube-mult` `unpow-prod-down` `pow1/3` `sqrt-div` `unpow3` `cube-prod` `rem-cbrt-cube` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `flip-+`

Counts

4 → 57

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)))
2.0ms	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))
2.0ms	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

series254.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
143.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
37.0ms	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))
32.0ms	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

simplify79.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (72.0ms)

Iter	Nodes	Cost
0	201	443
1	502	413
2	1079	413
3	2495	413
4	5002	412

prune368.0ms

Filtered

69 candidates to 54 candidates (78.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	69	8	77

Merged error: 17.4b

Counts

77 → 8

regimes302.0ms

Accuracy

77.6% (3.1b remaining)

Error of 22.4b against oracle of 19.3b and baseline of 33.2b

bsearch135.0ms

Steps

Iters	Range		Point
9	-1.6208289690593208e-305	3.4236090926054554e-305	-5.61375364858452e-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	2230×	body	1280	valid
708.0ms	7944×	body	80	valid
604.0ms	1442×	body	640	valid
159.0ms	560×	body	320	valid
67.0ms	44×	body	2560	valid
45.0ms	242×	body	160	valid