Details

sample79.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 62.473122%

Results

10.0ms	200×	body	80	valid
7.0ms	24×	body	2560	valid
3.0ms	9×	body	5120	valid
2.0ms	9×	body	1280	valid
1.0ms	8×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	3×	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

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: 36.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
27.6b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

7.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series38.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
10.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify75.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	247	351
1	781	333
2	2656	327
3	5001	325

prune107.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	8	50

Merged error: 18.7b

Counts

50 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
6.1b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
28.5b	(cbrt (+ (* re re) (* im im)))
28.5b	(cbrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

8.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
8.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series104.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
28.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
22.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))

simplify127.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	355	1000
1	1235	940
2	4815	899
3	5002	885

prune149.0ms

Filtered

66 candidates to 77 candidates (-16.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	1	5	6
Picked	1	0	1
Done	1	0	1
Total	77	8	85

Merged error: 18.7b

Counts

85 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

5.1b	(exp (log (cbrt (+ (* re re) (* im im)))))
13.2b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
28.5b	(cbrt (+ (* re re) (* im im)))
28.5b	(cbrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

5.0ms	(exp (log (cbrt (+ (* re re) (* im im)))))
11.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series92.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(exp (log (cbrt (+ (* re re) (* im im)))))
29.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
22.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))

simplify93.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	334	795
1	1008	725
2	3209	668
3	5002	636

prune167.0ms

Filtered

64 candidates to 70 candidates (-9.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	70	8	78

Merged error: 18.7b

Counts

78 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

28.5b	(cbrt (+ (* re re) (* im im)))
28.5b	(cbrt (+ (* re re) (* im im)))
28.5b	(cbrt (+ (* re re) (* im im)))
28.5b	(cbrt (+ (* re re) (* im im)))

rewrite19.0ms

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:

6.0ms	(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)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	151	560
1	426	524
2	1225	500
3	5002	468

prune126.0ms

Filtered

56 candidates to 64 candidates (-14.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	64	8	72

Merged error: 18.7b

Counts

72 → 8

regimes292.0ms

Accuracy

58.7% (9.5b remaining)

Error of 27.1b against oracle of 17.7b and baseline of 40.6b

bsearch45.0ms

Steps

Iters	Range		Point
10	2.8916002143913826e+113	9.908310096609737e+123	2.641426491877618e+121
7	2.5303928779853354e-191	3.4722655433964892e-189	3.2710593673458567e-191

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	55
1	50	55

end0.0ms

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 62.473122%

Results

301.0ms	6024×	body	80	valid
192.0ms	672×	body	2560	valid
115.0ms	490×	body	1280	valid
102.0ms	295×	body	5120	valid
56.0ms	282×	body	640	valid
20.0ms	148×	body	320	valid
8.0ms	89×	body	160	valid

Details

sample79.0ms

simplify5.0ms

prune3.0ms

localize10.0ms

rewrite18.0ms

series38.0ms

simplify75.0ms

prune107.0ms

localize14.0ms

rewrite25.0ms

series104.0ms

simplify127.0ms

prune149.0ms

localize19.0ms

rewrite25.0ms

series92.0ms

simplify93.0ms

prune167.0ms

localize25.0ms

rewrite19.0ms

series83.0ms

simplify51.0ms

prune126.0ms

regimes292.0ms

bsearch45.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling