Details

sample43.0ms

Algorithm

intervals

Results

27.0ms

699×

body

valid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	8
1	41	8
2	67	8
3	119	8
4	309	8
5	1485	8
6	5002	8

prune2.0ms

Filtered

1 candidates to 0 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 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

2×	`+-commutative` `flip3-+` `associate-r` `*-commutative` `flip-+`
1×	`pow-to-exp` `sqr-pow`

Counts

4 → 11

Calls

4 calls:

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

series215.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
26.0ms	(+ (* a a) (* b b))
26.0ms	(* 4.0 (* b b))
100.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify77.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	173	135
1	695	127
2	2430	127
3	5001	127

prune54.0ms

Filtered

23 candidates to 16 candidates (69.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	21	2	23
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	2	24

Merged error: 0.0b

Counts

24 → 2

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 2 (* (pow a 2) (pow b 2)))
1.8b	(* (pow a 2) (pow b 2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`associate-r`
12×	`unpow2` `sqr-pow`
8×	`unswap-sqr`
4×	`associate-l`
3×	`*-commutative`
2×	`pow-to-exp`
1×	`pow-prod-down` `prod-exp`

Counts

2 → 22

Calls

2 calls:

9.0ms	(* 2 (* (pow a 2) (pow b 2)))
8.0ms	(* (pow a 2) (pow b 2))

series71.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(* 2 (* (pow a 2) (pow b 2)))
37.0ms	(* (pow a 2) (pow b 2))

simplify35.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	77	62
1	181	62
2	820	62
3	5001	62

prune64.0ms

Filtered

28 candidates to 19 candidates (67.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	28	2	30

Merged error: 0.0b

Counts

30 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (* (pow a 2) (pow b 2)))
0.0b	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
1.8b	(* (pow a 2) (pow b 2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

16×	`associate-r`
12×	`unpow2` `sqr-pow`
8×	`unswap-sqr`
5×	`*-commutative`
4×	`associate-l`
2×	`+-commutative` `pow-to-exp` `associate-+l+`
1×	`flip3-+` `pow-prod-down` `prod-exp` `flip-+`

Counts

4 → 30

Calls

4 calls:

5.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
10.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
3.0ms	(* 4.0 (* b b))
4.0ms	(* (pow a 2) (pow b 2))

series150.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
57.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
26.0ms	(* 4.0 (* b b))
31.0ms	(* (pow a 2) (pow b 2))

simplify135.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	153	173
1	527	167
2	2803	151
3	5001	151

prune85.0ms

Filtered

42 candidates to 27 candidates (64.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	42	2	44

Merged error: 0.0b

Counts

44 → 2

regimes35.0ms

Accuracy

93.7% (0.1b remaining)

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

bsearch108.0ms

Steps

Iters	Range		Point
8	5.206592823702773e-46	6.8203431504564e-43	1.2385758517046966e-45
10	-0.0011167250079306748	-1.2209559826642226e-16	-0.000107404362338187

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	19
1	39	19

end0.0ms

sample1.3s

Algorithm

intervals

Results

874.0ms

20696×

body

valid