Details

sample61.0ms

Algorithm

intervals

Results

42.0ms

614×

body

valid

simplify99.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize20.0ms

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)

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

series61.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (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)))
23.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify86.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (74.0ms)

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

prune161.0ms

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

localize20.0ms

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)

rewrite15.0ms

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (+ 1.0 a))
6.0ms	(cbrt (+ 1.0 a))
8.0ms	(cbrt (+ 1.0 a))
21.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify109.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (102.0ms)

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

prune178.0ms

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

localize20.0ms

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)))))))

rewrite25.0ms

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)
8.0ms	(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)))))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (+ (* a a) (* b b)) 2.0)
25.0ms	(pow (+ (* a a) (* b b)) 2.0)
31.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
31.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (31.0ms)

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

prune216.0ms

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

localize30.0ms

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)))

rewrite31.0ms

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:

19.0ms	(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)))
4.0ms	(cbrt (+ (* a a) (* b b)))
4.0ms	(cbrt (+ (* a a) (* b b)))

series109.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(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)))))))
22.0ms	(cbrt (+ (* a a) (* b b)))
21.0ms	(cbrt (+ (* a a) (* b b)))
21.0ms	(cbrt (+ (* a a) (* b b)))

simplify45.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (34.0ms)

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

prune240.0ms

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

regimes215.0ms

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

Results

1.4s

20105×

body

valid

Details

sample61.0ms

simplify99.0ms

prune3.0ms

localize20.0ms

rewrite28.0ms

series61.0ms

simplify86.0ms

prune161.0ms

localize20.0ms

rewrite15.0ms

series42.0ms

simplify109.0ms

prune178.0ms

localize20.0ms

rewrite25.0ms

series108.0ms

simplify43.0ms

prune216.0ms

localize30.0ms

rewrite31.0ms

series109.0ms

simplify45.0ms

prune240.0ms

regimes215.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.9s

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