Details

sample40.0ms

Algorithm

intervals

Results

17.0ms	394×	body	80	valid
6.0ms	169×	body	80	nan

simplify106.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	7
1	53	5
2	106	5
3	269	5
4	904	5
5	3967	5
6	5001	5

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 1.2b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(* a (pow k m))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
1.2b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

3×	`+-commutative` `flip3-+` `flip-+` `associate-/l*`
2×	`associate-+l+` `associate-r` `associate-/r/` `*-commutative` `sqr-pow`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 18

Calls

4 calls:

3.0ms	(+ 1.0 (* 10.0 k))
2.0ms	(* a (pow k m))
5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
7.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ 1.0 (* 10.0 k))
58.0ms	(* a (pow k m))
19.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
124.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify99.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	278	209
1	1025	189
2	4318	163
3	5001	147

prune90.0ms

Filtered

30 candidates to 24 candidates (80.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	29	3	32

Merged error: 0.0b

Counts

32 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma k k (fma k 10.0 1.0))
0.0b	(fma k 10.0 1.0)
0.2b	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
2.4b	(/ (fma k k (fma k 10.0 1.0)) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`div-inv`
3×	`frac-2neg` `clear-num` `associate-/r/`
2×	`fma-udef` `sqr-pow`
1×	`times-frac` `associate-/r` `associate-/l`

Counts

4 → 14

Calls

4 calls:

1.0ms	(fma k k (fma k 10.0 1.0))
1.0ms	(fma k 10.0 1.0)
3.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
2.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

series211.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(fma k k (fma k 10.0 1.0))
31.0ms	(fma k 10.0 1.0)
113.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
45.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

simplify76.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	197	155
1	640	149
2	2942	139
3	5001	119

prune73.0ms

Filtered

26 candidates to 19 candidates (73.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	25	1	26
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	26	3	29

Merged error: 0b

Counts

29 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (/ 10.0 a) k (/ 1.0 a))
0.2b	(/ (pow k m) (fma (/ k a) k (fma (/ 10.0 a) k (/ 1.0 a))))
2.8b	(fma (/ k a) k (fma (/ 10.0 a) k (/ 1.0 a)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

2×	`fma-udef`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*` `sqr-pow`

Counts

3 → 6

Calls

3 calls:

1.0ms	(fma (/ 10.0 a) k (/ 1.0 a))
3.0ms	(/ (pow k m) (fma (/ k a) k (fma (/ 10.0 a) k (/ 1.0 a))))
1.0ms	(fma (/ k a) k (fma (/ 10.0 a) k (/ 1.0 a)))

series189.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(fma (/ 10.0 a) k (/ 1.0 a))
102.0ms	(/ (pow k m) (fma (/ k a) k (fma (/ 10.0 a) k (/ 1.0 a))))
37.0ms	(fma (/ k a) k (fma (/ 10.0 a) k (/ 1.0 a)))

simplify66.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	174	134
1	568	123
2	2444	116
3	5002	97

prune39.0ms

Filtered

15 candidates to 9 candidates (60.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	15	0	15
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	15	3	18

Merged error: 0b

Counts

18 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (/ a k) (pow (/ 1 k) (* -1 m))) k)
4.0b	(* (/ a k) (pow (/ 1 k) (* -1 m)))
4.9b	(/ a (pow k 3))
9.1b	(/ (* (/ a (pow k 3)) 1) (pow (/ 1 k) m))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

14×	`div-inv`
13×	`associate-/l/`
11×	`associate-*l/`
10×	`pow-neg` `mul-1-neg`
8×	`frac-2neg` `clear-num` `associate-/l*` `sqr-pow`
6×	`frac-times` `unpow-prod-down` `times-frac` `associate-/r*`
5×	`associate-l` `*-commutative`
4×	`associate-r`
2×	`unpow3` `associate-*r/` `un-div-inv`

Counts

4 → 52

Calls

4 calls:

7.0ms	(/ (* (/ a k) (pow (/ 1 k) (* -1 m))) k)
5.0ms	(* (/ a k) (pow (/ 1 k) (* -1 m)))
2.0ms	(/ a (pow k 3))
7.0ms	(/ (* (/ a (pow k 3)) 1) (pow (/ 1 k) m))

series299.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (* (/ a k) (pow (/ 1 k) (* -1 m))) k)
88.0ms	(* (/ a k) (pow (/ 1 k) (* -1 m)))
31.0ms	(/ a (pow k 3))
93.0ms	(/ (* (/ a (pow k 3)) 1) (pow (/ 1 k) m))

simplify46.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	310	311
1	1735	304
2	5001	299

prune260.0ms

Filtered

64 candidates to 56 candidates (87.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	64	3	67

Merged error: 0b

Counts

67 → 3

regimes87.0ms

Accuracy

97.2% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.1b

bsearch26.0ms

Steps

Iters	Range		Point
4	1.2197657103371039e+78	2.1249675234717626e+78	1.7244579000634613e+78

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	22
1	45	22
2	45	22

end0.0ms

sample1000.0ms

Algorithm

intervals

Results

511.0ms	11877×	body	80	valid
150.0ms	4260×	body	80	nan