Details

analyze213.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 60.975638%

Guaranteed chance to sample good point: 96.28125%

sample27.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify94.0ms

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)
0.5b	(* (* 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))))))
8.0ms	(* (* a a) (+ 1.0 a))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series62.0ms

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))))))
7.0ms	(* (* a a) (+ 1.0 a))
22.0ms	(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

prune151.0ms

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:

0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
8.7b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.7b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite30.0ms

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:

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

series75.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
7.0ms	(* (* 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)))))))
30.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

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

prune219.0ms

Filtered

60 candidates to 92 candidates (-53.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	92	5	97

Merged error: 0.0b

Counts

97 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ 1.0 a))
0.2b	(cbrt (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

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

series41.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(cbrt (+ 1.0 a))
6.0ms	(cbrt (+ 1.0 a))
22.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	434	584
1	1678	532
2	5001	515

prune197.0ms

Filtered

59 candidates to 82 candidates (-39.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	82	5	87

Merged error: 0b

Counts

87 → 5

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ 1.0 a))
0.2b	(cbrt (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (+ 1.0 a))
6.0ms	(cbrt (+ 1.0 a))
22.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	434	584
1	1678	532
2	5001	515

prune201.0ms

Filtered

59 candidates to 82 candidates (-39.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	82	5	87

Merged error: 0b

Counts

87 → 5

regimes254.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	27
1	38	27

end0.0ms

analyze209.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 60.975638%

Guaranteed chance to sample good point: 96.28125%

sample649.0ms

Algorithm

intervals

Results

517.0ms	8000×	body	80	valid
0.0ms	3×	body	80	invalid

Details

analyze213.0ms

sample27.0ms

simplify94.0ms

prune3.0ms

localize16.0ms

rewrite28.0ms

series62.0ms

simplify72.0ms

prune151.0ms

localize20.0ms

rewrite30.0ms

series75.0ms

simplify47.0ms

prune219.0ms

localize20.0ms

rewrite19.0ms

series41.0ms

simplify48.0ms

prune197.0ms

localize31.0ms

rewrite20.0ms

series42.0ms

simplify48.0ms

prune201.0ms

regimes254.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze209.0ms

sample649.0ms

Profiling