Details

sample59.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

24.0ms	358×	body	80	invalid
16.0ms	256×	body	80	valid

simplify88.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	15
1	161	15
2	459	15
3	1323	15
4	2992	15
5	5001	15

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: 0.2b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b	(* (* a a) (+ 1.0 a))
0.1b	(* (* b b) (- 1.0 (* 3.0 a)))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
3×	`unpow-prod-down` `pow-unpow`
2×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

7.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
7.0ms	(* (* a a) (+ 1.0 a))
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
7.0ms	(pow (+ (* a a) (* b b)) 2.0)

series57.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
5.0ms	(* (* a a) (+ 1.0 a))
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
21.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify69.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	547	721
1	2714	641
2	5001	637

prune149.0ms

Filtered

61 candidates to 91 candidates (-49.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	5	92

Merged error: 0.0b

Counts

92 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ 1.0 a))
0.2b	(cbrt (+ 1.0 a))
0.2b	(cbrt (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
12×	`cbrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`

Counts

4 → 59

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 a))
3.0ms	(cbrt (+ 1.0 a))
3.0ms	(cbrt (+ 1.0 a))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series42.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(cbrt (+ 1.0 a))
6.0ms	(cbrt (+ 1.0 a))
6.0ms	(cbrt (+ 1.0 a))
21.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify113.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	283	541
1	892	515
2	3552	449
3	5001	439

prune172.0ms

Filtered

54 candidates to 71 candidates (-31.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	72	4	76

Merged error: 0.0b

Counts

76 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
8.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`add-exp-log` `unpow-prod-down` `pow-unpow` `sqrt-prod`
4×	`sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `flip-+` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

7.0ms	(pow (+ (* a a) (* b b)) 2.0)
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
6.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series105.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (+ (* a a) (* b b)) 2.0)
21.0ms	(pow (+ (* a a) (* b b)) 2.0)
30.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
30.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify42.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	290	994
1	1071	958
2	5001	942

prune224.0ms

Filtered

58 candidates to 76 candidates (-31.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	75	5	80

Merged error: 0.0b

Counts

80 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

8.2b	(sqrt (+ (* (pow (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b)))) 2.0) (pow (cbrt (+ (* a a) (* b b))) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.7b	(cbrt (+ (* a a) (* b b)))
8.7b	(cbrt (+ (* a a) (* b b)))
8.7b	(cbrt (+ (* a a) (* b b)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

15.0ms	(sqrt (+ (* (pow (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b)))) 2.0) (pow (cbrt (+ (* a a) (* b b))) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
4.0ms	(cbrt (+ (* a a) (* b b)))
3.0ms	(cbrt (+ (* a a) (* b b)))
3.0ms	(cbrt (+ (* a a) (* b b)))

series99.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (* (pow (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b)))) 2.0) (pow (cbrt (+ (* a a) (* b b))) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
20.0ms	(cbrt (+ (* a a) (* b b)))
21.0ms	(cbrt (+ (* a a) (* b b)))
23.0ms	(cbrt (+ (* a a) (* b b)))

simplify41.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	334	1035
1	1226	979
2	5001	961

prune230.0ms

Filtered

63 candidates to 66 candidates (-4.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	66	5	71

Merged error: 0b

Counts

71 → 5

regimes206.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	32
1	29	32

end0.0ms

sample1.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

865.0ms	12105×	body	80	invalid
530.0ms	8000×	body	80	valid

Details

sample59.0ms

simplify88.0ms

prune3.0ms

localize15.0ms

rewrite29.0ms

series57.0ms

simplify69.0ms

prune149.0ms

localize19.0ms

rewrite14.0ms

series42.0ms

simplify113.0ms

prune172.0ms

localize19.0ms

rewrite24.0ms

series105.0ms

simplify42.0ms

prune224.0ms

localize29.0ms

rewrite26.0ms

series99.0ms

simplify41.0ms

prune230.0ms

regimes206.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling