Details

analyze137.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

sample25.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify86.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4906	31
1	4906	31

prune13.0ms

Filtered

1 candidates to 1 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: 0.2b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* a a) (+ 1.0 a))
0.1b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.2b	(* (* 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×	`associate-*r/`
3×	`distribute-rgt-in` `unpow-prod-down` `pow-unpow` `distribute-lft-in`
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 → 77

Calls

4 calls:

7.0ms	(* (* a a) (+ 1.0 a))
8.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series58.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (* a a) (+ 1.0 a))
25.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
21.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify32.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5881	1271

prune156.0ms

Filtered

61 candidates to 89 candidates (-45.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	85	6	91

Merged error: 0.0b

Counts

91 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

7.0ms	(* b (* b (- 1.0 (* a 3.0))))
6.0ms	(* b (- 1.0 (* a 3.0)))
14.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (- (* 4.0 (+ (* a (* a (+ a 1.0))) (* b (* b (- 1.0 (* a 3.0)))))) 1.0))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series58.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* b (* b (- 1.0 (* a 3.0))))
7.0ms	(* b (- 1.0 (* a 3.0)))
24.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (- (* 4.0 (+ (* a (* a (+ a 1.0))) (* b (* b (- 1.0 (* a 3.0)))))) 1.0))
21.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5241	1417

prune146.0ms

Filtered

60 candidates to 92 candidates (-53.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	92	6	98

Merged error: 0.0b

Counts

98 → 6

localize24.0ms

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)
10.8b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ a 1.0)))))))
10.8b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ a 1.0)))))))

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:

5.0ms	(pow (+ (* a a) (* b b)) 2.0)
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
6.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ a 1.0)))))))
7.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ a 1.0)))))))

series103.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (+ (* a a) (* b b)) 2.0)
22.0ms	(pow (+ (* a a) (* b b)) 2.0)
30.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ a 1.0)))))))
30.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ a 1.0)))))))

simplify38.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5098	1766

prune227.0ms

Filtered

58 candidates to 76 candidates (-31.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	76	6	82

Merged error: 0.0b

Counts

82 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

10.8b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ a 1.0)))))))
21.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
21.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
21.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 60

Calls

4 calls:

7.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ a 1.0)))))))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series133.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ a 1.0)))))))
33.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
33.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
36.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify35.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5040	1482

prune308.0ms

Filtered

62 candidates to 72 candidates (-16.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	6	78

Merged error: 0.0b

Counts

78 → 6

regimes159.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	67	63
1	67	63

end0.0ms

sample666.0ms

Algorithm

intervals

Results

535.0ms	8000×	body	80	valid
0.0ms	5×	body	80	invalid

Details

analyze137.0ms

sample25.0ms

simplify86.0ms

prune13.0ms

localize16.0ms

rewrite29.0ms

series58.0ms

simplify32.0ms

prune156.0ms

localize18.0ms

rewrite34.0ms

series58.0ms

simplify66.0ms

prune146.0ms

localize24.0ms

rewrite24.0ms

series103.0ms

simplify38.0ms

prune227.0ms

localize30.0ms

rewrite21.0ms

series133.0ms

simplify35.0ms

prune308.0ms

regimes159.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample666.0ms

Profiling