Details

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 74.609375%

Results

9.0ms	191×	body	80	valid
5.0ms	20×	body	2560	valid
4.0ms	17×	body	1280	valid
4.0ms	11×	body	5120	valid
1.0ms	7×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	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: 39.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.2b	(- (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

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

series41.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify89.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	234	381
1	812	362
2	3077	355
3	5001	353

prune99.0ms

Filtered

42 candidates to 52 candidates (-23.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	6	53

Merged error: 16.7b

Counts

53 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3)
1.2b	(- (sqrt (+ (* re re) (* im im))) re)
13.5b	(cbrt (pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`cbrt-prod`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`pow1`
8×	`unpow-prod-down` `cube-prod` `sqrt-prod`
6×	`sqrt-div` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`cube-div` `pow-pow` `associate-*r/`
3×	`pow-unpow` `flip3--` `sqrt-pow1` `flip--`
2×	`cube-mult` `cbrt-div` `pow1/2` `unpow3` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `flip3-+` `pow1/3` `diff-log` `pow-prod-down` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `flip-+` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 86

Calls

4 calls:

10.0ms	(pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3)
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(cbrt (pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3))
4.0ms	(sqrt (+ (* re re) (* im im)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3)
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
22.0ms	(cbrt (pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	430	918
1	1846	892
2	5002	879

prune144.0ms

Filtered

63 candidates to 98 candidates (-55.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	96	8	104

Merged error: 16.7b

Counts

104 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

7.8b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
14.5b	(cbrt (pow (sqrt (* 2.0 (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re))) 3))
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
12×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-prod`
6×	`pow1` `sqrt-div` `add-log-exp`
4×	`add-exp-log` `unpow-prod-down` `cube-prod` `add-cbrt-cube`
2×	`cube-div` `rem-sqrt-square` `cbrt-div` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube` `difference-of-squares` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

14.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
7.0ms	(cbrt (pow (sqrt (* 2.0 (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re))) 3))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
22.0ms	(cbrt (pow (sqrt (* 2.0 (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re))) 3))
7.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify122.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	338	1091
1	1191	1008
2	4656	998
3	5002	998

prune139.0ms

Filtered

60 candidates to 80 candidates (-33.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	79	9	88

Merged error: 16.7b

Counts

88 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im 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 (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series23.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify136.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 5 (130.0ms)

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

prune186.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	72	9	81

Merged error: 16.7b

Counts

81 → 9

regimes643.0ms

Accuracy

59.5% (8.5b remaining)

Error of 26.0b against oracle of 17.5b and baseline of 38.5b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	49
1	51	49

end0.0ms

sample2.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 74.609375%

Results

303.0ms	6109×	body	80	valid
181.0ms	648×	body	2560	valid
109.0ms	477×	body	1280	valid
94.0ms	272×	body	5120	valid
47.0ms	265×	body	640	valid
23.0ms	148×	body	320	valid
7.0ms	81×	body	160	valid

Details

sample1.1s

simplify7.0ms

prune3.0ms

localize10.0ms

rewrite19.0ms

series41.0ms

simplify89.0ms

prune99.0ms

localize14.0ms

rewrite27.0ms

series97.0ms

simplify55.0ms

prune144.0ms

localize16.0ms

rewrite31.0ms

series43.0ms

simplify122.0ms

prune139.0ms

localize22.0ms

rewrite17.0ms

series23.0ms

simplify136.0ms

prune186.0ms

regimes643.0ms

bsearch3.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling