Details

analyze141.0ms

Algorithm: search

sample30.0ms

Algorithm

intervals

Results

21.0ms

256×

body

valid

simplify96.0ms

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

localize16.0ms

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))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.8b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite28.0ms

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

series61.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (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))
24.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify72.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (63.0ms)

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

prune165.0ms

Filtered

61 candidates to 91 candidates (-49.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	84	7	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	7	92

Merged error: 0.0b

Counts

92 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (* b b) (- 1.0 (* 3.0 a)))
0.8b	(* (* b b) (- 1.0 (* 3.0 a)))
9.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div` `associate-*r/` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l` `*-commutative` `flip--` `flip-+` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

12.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
12.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
10.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series84.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
9.0ms	(* (* 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)))))))
38.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	333	1080
1	1424	980
2	5002	978

prune233.0ms

Filtered

60 candidates to 92 candidates (-53.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	92	7	99

Merged error: 0.0b

Counts

99 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (* b b) (- 1.0 (* 3.0 a)))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.6b	(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×	`pow1` `add-exp-log` `unpow-prod-down` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

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

series111.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
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))

simplify37.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	295	702
1	1114	636
2	5001	618

prune244.0ms

Filtered

64 candidates to 82 candidates (-28.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	83	6	89

Merged error: 0.0b

Counts

89 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

10.0b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
10.0b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

34×	`cbrt-prod`
18×	`unpow-prod-down`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

5.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
5.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series137.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
35.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
34.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
35.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	212	832
1	481	780
2	1535	756
3	5002	726

prune260.0ms

Filtered

62 candidates to 78 candidates (-25.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	78	6	84

Merged error: 0.0b

Counts

84 → 6

regimes229.0ms

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

analyze135.0ms

Algorithm: search

sample661.0ms

Algorithm

intervals

Results

533.0ms	8000×	body	80	valid
0.0ms	6×	body	80	invalid

Details

analyze141.0ms

sample30.0ms

simplify96.0ms

prune3.0ms

localize16.0ms

rewrite28.0ms

series61.0ms

simplify72.0ms

prune165.0ms

localize25.0ms

rewrite48.0ms

series84.0ms

simplify45.0ms

prune233.0ms

localize21.0ms

rewrite21.0ms

series111.0ms

simplify37.0ms

prune244.0ms

localize28.0ms

rewrite21.0ms

series137.0ms

simplify51.0ms

prune260.0ms

regimes229.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze135.0ms

sample661.0ms

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