Details

sample41.0ms

Algorithm

intervals

Results

18.0ms	383×	body	80	valid
6.0ms	159×	body	80	nan

simplify104.0ms

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: 1.3b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (pow k m))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(+ 1.0 (* 10.0 k))
1.3b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite20.0ms

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:

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

series227.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* a (pow k m))
18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
31.0ms	(+ 1.0 (* 10.0 k))
116.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify95.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (91.0ms)

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

prune87.0ms

Filtered

30 candidates to 24 candidates (80.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	29	3	32

Merged error: 0.0b

Counts

32 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(/ (* a 1) (pow (/ 1 k) m))
0.0b	(+ 1.0 (* 10.0 k))
1.3b	(/ (/ (* a 1) (pow (/ 1 k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`div-inv` `associate-/l*`
8×	`times-frac`
7×	`associate-/l/`
6×	`unpow-prod-down` `*-commutative` `sqr-pow`
4×	`associate-/r*`
3×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `flip-+`
2×	`associate-+l+` `associate-/r/`

Counts

4 → 36

Calls

4 calls:

5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
4.0ms	(/ (* a 1) (pow (/ 1 k) m))
3.0ms	(+ 1.0 (* 10.0 k))
8.0ms	(/ (/ (* a 1) (pow (/ 1 k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
75.0ms	(/ (* a 1) (pow (/ 1 k) m))
32.0ms	(+ 1.0 (* 10.0 k))
148.0ms	(/ (/ (* a 1) (pow (/ 1 k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify44.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	342	314
1	1597	274
2	5001	266

prune140.0ms

Filtered

48 candidates to 38 candidates (79.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	48	3	51

Merged error: 0.0b

Counts

51 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* a 1) (pow (/ 1 k) m))
0.0b	(fma 10.0 k 1.0)
0.1b	(/ 1 (fma k k (fma 10.0 k 1.0)))
1.3b	(* (/ (* a 1) (pow (/ 1 k) m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

21×	`frac-times`
15×	`clear-num`
14×	`frac-2neg`
13×	`div-inv`
10×	`associate-/r` `-commutative` `associate-/l*`
9×	`unpow-prod-down` `sqr-pow`
8×	`times-frac`
7×	`associate-*l/`
5×	`associate-l`
3×	`associate-*r/`
2×	`un-div-inv`
1×	`associate-r` `fma-udef` `inv-pow`

Counts

4 → 56

Calls

4 calls:

7.0ms	(/ (* a 1) (pow (/ 1 k) m))
1.0ms	(fma 10.0 k 1.0)
2.0ms	(/ 1 (fma k k (fma 10.0 k 1.0)))
8.0ms	(* (/ (* a 1) (pow (/ 1 k) m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (* a 1) (pow (/ 1 k) m))
30.0ms	(fma 10.0 k 1.0)
41.0ms	(/ 1 (fma k k (fma 10.0 k 1.0)))
146.0ms	(* (/ (* a 1) (pow (/ 1 k) m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

simplify48.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	360	386
1	1698	365
2	5002	363

prune150.0ms

Filtered

68 candidates to 43 candidates (63.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	67	4	71

Merged error: 0.0b

Counts

71 → 4

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (* a 1) (pow (/ 1 k) m))
0.1b	(fma (pow k 2) 99.0 (- 1.0 (* 10.0 k)))
11.5b	(* (/ (* a 1) (pow (/ 1 k) m)) (fma (pow k 2) 99.0 (- 1.0 (* 10.0 k))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

8×	`times-frac` `div-inv`
7×	`associate-l/` `-commutative`
6×	`unpow-prod-down` `sqr-pow`
5×	`associate-l`
4×	`associate-/r` `associate-/l`
3×	`fma-udef`
2×	`frac-2neg` `clear-num`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

3 → 27

Calls

3 calls:

4.0ms	(/ (* a 1) (pow (/ 1 k) m))
1.0ms	(fma (pow k 2) 99.0 (- 1.0 (* 10.0 k)))
6.0ms	(* (/ (* a 1) (pow (/ 1 k) m)) (fma (pow k 2) 99.0 (- 1.0 (* 10.0 k))))

series229.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (* a 1) (pow (/ 1 k) m))
23.0ms	(fma (pow k 2) 99.0 (- 1.0 (* 10.0 k)))
131.0ms	(* (/ (* a 1) (pow (/ 1 k) m)) (fma (pow k 2) 99.0 (- 1.0 (* 10.0 k))))

simplify36.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	226	235
1	1077	227
2	5001	212

prune94.0ms

Filtered

36 candidates to 27 candidates (75.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	36	4	40

Merged error: 0.0b

Counts

40 → 4

regimes72.0ms

Accuracy

96.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.9b

bsearch53.0ms

Steps

Iters	Range		Point
8	2.780302897405976e+149	1.3412804874082685e+153	3.2205424189704093e+149

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	24
1	47	24
2	47	24

end0.0ms

sample1.1s

Algorithm

intervals

Results

569.0ms	11880×	body	80	valid
162.0ms	4240×	body	80	nan