Details

analyze83.0ms

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%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4828	17
1	4828	17

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a a) (* b b))
0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

4.0ms	(+ (* a a) (* b b))
7.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
5.0ms	(* 4.0 (* b b))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series48.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a a) (* b b))
15.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
3.0ms	(* 4.0 (* b b))
25.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify34.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5434	782

prune113.0ms

Filtered

52 candidates to 70 candidates (-34.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	3	71

Merged error: 0b

Counts

71 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow b 4) (+ (pow a 4) (* a (* a (* b (* b 2))))))
0.0b	(+ (pow a 4) (* a (* a (* b (* b 2)))))
0.4b	(* a (* b (* b 2)))
0.5b	(* a (* a (* b (* b 2))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-log-exp`
8×	`*-un-lft-identity`
6×	`add-sqr-sqrt` `add-cube-cbrt` `associate-l`
4×	`sum-log`
2×	`+-commutative` `flip3-+` `associate-r` `*-commutative` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 70

Calls

4 calls:

9.0ms	(+ (pow b 4) (+ (pow a 4) (* a (* a (* b (* b 2))))))
5.0ms	(+ (pow a 4) (* a (* a (* b (* b 2)))))
6.0ms	(* a (* b (* b 2)))
9.0ms	(* a (* a (* b (* b 2))))

series37.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (pow b 4) (+ (pow a 4) (* a (* a (* b (* b 2))))))
9.0ms	(+ (pow a 4) (* a (* a (* b (* b 2)))))
9.0ms	(* a (* b (* b 2)))
7.0ms	(* a (* a (* b (* b 2))))

simplify52.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4966	1002
1	4966	1002

prune108.0ms

Filtered

45 candidates to 82 candidates (-82.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	82	3	85

Merged error: 0b

Counts

85 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (pow b (* 2.0 2)) (* a (* a (* 2.0 (pow b 2.0))))) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
0.4b	(* a (* 2.0 (pow b 2.0)))
0.5b	(* a (* a (* 2.0 (pow b 2.0))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
23×	`add-cbrt-cube`
22×	`prod-exp`
16×	`pow1`
12×	`cbrt-unprod`
9×	`associate-l` `add-log-exp`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity` `pow-prod-down`
3×	`associate-r` `sum-log` `*-commutative`
2×	`pow-to-exp` `pow-exp`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

9.0ms	(+ (+ (pow b (* 2.0 2)) (* a (* a (* 2.0 (pow b 2.0))))) (* 4.0 (* b b)))
5.0ms	(* 4.0 (* b b))
6.0ms	(* a (* 2.0 (pow b 2.0)))
8.0ms	(* a (* a (* 2.0 (pow b 2.0))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (+ (pow b (* 2.0 2)) (* a (* a (* 2.0 (pow b 2.0))))) (* 4.0 (* b b)))
3.0ms	(* 4.0 (* b b))
32.0ms	(* a (* 2.0 (pow b 2.0)))
37.0ms	(* a (* a (* 2.0 (pow b 2.0))))

simplify48.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4919	971
1	4919	971

prune131.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	85	3	88

Merged error: 0b

Counts

88 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* b (* b 4.0)))
0.2b	(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* b (* b 4.0))) 3)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
27.5b	(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* b (* b 4.0))) 3))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
6×	`pow1` `add-exp-log` `pow-unpow` `cube-prod` `add-log-exp`
5×	`add-cbrt-cube`
4×	`cube-div`
3×	`flip3-+` `flip-+` `sqr-pow`
2×	`cube-mult` `pow-to-exp` `cbrt-div` `pow-pow` `unpow3` `pow-exp`
1×	`+-commutative` `pow1/3` `sum-log` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 76

Calls

4 calls:

7.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* b (* b 4.0)))
9.0ms	(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* b (* b 4.0))) 3)
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
8.0ms	(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* b (* b 4.0))) 3))

series136.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* b (* b 4.0)))
84.0ms	(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* b (* b 4.0))) 3)
21.0ms	(pow (+ (* a a) (* b b)) 2.0)
15.0ms	(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* b (* b 4.0))) 3))

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4956	1703
1	4956	1703

prune129.0ms

Filtered

58 candidates to 88 candidates (-51.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	88	3	91

Merged error: 0b

Counts

91 → 3

regimes134.0ms

Accuracy

95.1% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	48
1	56	48

end0.0ms

sample501.0ms

Algorithm

intervals

Results

363.0ms	8000×	body	80	valid
0.0ms	5×	body	80	invalid

Details

analyze83.0ms

sample20.0ms

simplify66.0ms

prune7.0ms

localize10.0ms

rewrite22.0ms

series48.0ms

simplify34.0ms

prune113.0ms

localize13.0ms

rewrite32.0ms

series37.0ms

simplify52.0ms

prune108.0ms

localize15.0ms

rewrite30.0ms

series89.0ms

simplify48.0ms

prune131.0ms

localize14.0ms

rewrite31.0ms

series136.0ms

simplify42.0ms

prune129.0ms

regimes134.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample501.0ms

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