Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	197×	body	80	valid
4.0ms	22×	body	2560	valid
2.0ms	14×	body	1280	valid
2.0ms	9×	body	5120	valid
1.0ms	6×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 37.2b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.5b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.1b	(+ (sqrt (+ (* re re) (* im im))) re)
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
11.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
180.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	274	428
1	986	391
2	3089	381
3	5002	379

prune188.0ms

Filtered

63 candidates to 52 candidates (82.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	7	64

Merged error: 18.2b

Counts

64 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

27.5b	(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
28.6b	(cbrt (+ (* re re) (* im im)))
28.6b	(cbrt (+ (* re re) (* im im)))
28.6b	(cbrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

16.0ms	(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
96.0ms	(cbrt (+ (* re re) (* im im)))
95.0ms	(cbrt (+ (* re re) (* im im)))
96.0ms	(cbrt (+ (* re re) (* im im)))

simplify192.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (172.0ms)

Iter	Nodes	Cost
0	287	1504
1	701	1463
2	3066	1446
3	5001	1379

prune282.0ms

Filtered

101 candidates to 64 candidates (63.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	100	8	108

Merged error: 18.1b

Counts

108 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

28.6b	(cbrt (+ (* re re) (* im im)))
28.6b	(cbrt (+ (* re re) (* im im)))
28.6b	(cbrt (+ (* re re) (* im im)))
28.6b	(cbrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (+ (* re re) (* im im)))
95.0ms	(cbrt (+ (* re re) (* im im)))
97.0ms	(cbrt (+ (* re re) (* im im)))
95.0ms	(cbrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	123	488
1	408	452
2	1386	444
3	5001	444

prune397.0ms

Filtered

64 candidates to 60 candidates (93.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	63	9	72

Merged error: 18.1b

Counts

72 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

28.6b	(cbrt (+ (* re re) (* im im)))
28.6b	(cbrt (+ (* re re) (* im im)))
28.6b	(cbrt (+ (* re re) (* im im)))
28.6b	(cbrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
8.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (+ (* re re) (* im im)))
95.0ms	(cbrt (+ (* re re) (* im im)))
95.0ms	(cbrt (+ (* re re) (* im im)))
96.0ms	(cbrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	123	488
1	408	452
2	1386	444
3	5001	444

prune418.0ms

Filtered

64 candidates to 60 candidates (93.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	64	9	73

Merged error: 18.1b

Counts

73 → 9

regimes226.0ms

Accuracy

58.5% (8.8b remaining)

Error of 26.7b against oracle of 17.9b and baseline of 39.0b

bsearch118.0ms

Steps

Iters	Range		Point
6	8.386220925578828e+143	4.316820422997054e+144	1.5282424607541283e+144
10	8.660844906217239e-175	7.0021986566734e-156	4.774322580768034e-170
9	3.2439511425214304e-251	1.5200205730203393e-242	1.7813720860167097e-247

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	37
1	52	37

end0.0ms

sample664.0ms

Algorithm

intervals

Results

197.0ms	5994×	body	80	valid
144.0ms	755×	body	2560	valid
68.0ms	448×	body	1280	valid
67.0ms	273×	body	5120	valid
37.0ms	286×	body	640	valid
14.0ms	153×	body	320	valid
5.0ms	91×	body	160	valid