Details

sample17.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	256×	pre	80	true

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (30.0ms)

Iter	Nodes	Cost
0	32	12
1	172	11
2	974	9
3	5001	8

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 16.8b

Counts

2 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

16.3b

(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-commutative`
8×	`times-frac`
6×	`associate-r`
4×	`associate-/r*`
2×	`associate-l/` `associate-/r/` `associate-/l`
1×	`flip3--` `frac-2neg` `clear-num` `flip--` `div-inv`

Counts

1 → 19

Calls

1 calls:

11.0ms

(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

series83.0ms

Counts

1 → 3

Calls

1 calls:

82.0ms

(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

simplify76.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	166	161
1	617	159
2	2793	156
3	5001	156

prune39.0ms

Filtered

22 candidates to 14 candidates (63.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	2	23

Merged error: 0.0b

Counts

23 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0)) (/ i (* 2.0 2.0)))
15.7b	(/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`frac-times`
12×	`clear-num`
11×	`frac-2neg`
8×	`associate-/r*`
5×	`associate-r/` `-commutative`
4×	`associate-/r/`
3×	`associate-l` `associate-*l/` `div-inv`
2×	`flip3--` `flip--`
1×	`associate-r` `un-div-inv`

Counts

2 → 34

Calls

2 calls:

10.0ms	(* (/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0)) (/ i (* 2.0 2.0)))
7.0ms	(/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0))

series163.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(* (/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0)) (/ i (* 2.0 2.0)))
82.0ms	(/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	281	273
1	1240	267
2	5001	263

prune70.0ms

Filtered

40 candidates to 28 candidates (70.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	40	2	42

Merged error: 0b

Counts

42 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* i (/ 1 (- (* (* 2.0 i) (* 2.0 i)) 1.0))) (/ i (* 2.0 2.0)))
0.3b	(/ 1 (- (* (* 2.0 i) (* 2.0 i)) 1.0))
15.4b	(* i (/ 1 (- (* (* 2.0 i) (* 2.0 i)) 1.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

26×	`associate-*r/`
25×	`frac-times`
22×	`clear-num`
15×	`un-div-inv`
14×	`frac-2neg`
12×	`associate-/r*`
9×	`*-commutative`
7×	`associate-r`
6×	`associate-/r/`
5×	`associate-l` `associate-*l/`
4×	`div-inv`
3×	`flip3--` `flip--`
1×	`inv-pow`

Counts

3 → 58

Calls

3 calls:

12.0ms	(* (* i (/ 1 (- (* (* 2.0 i) (* 2.0 i)) 1.0))) (/ i (* 2.0 2.0)))
7.0ms	(/ 1 (- (* (* 2.0 i) (* 2.0 i)) 1.0))
8.0ms	(* i (/ 1 (- (* (* 2.0 i) (* 2.0 i)) 1.0)))

series221.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(* (* i (/ 1 (- (* (* 2.0 i) (* 2.0 i)) 1.0))) (/ i (* 2.0 2.0)))
58.0ms	(/ 1 (- (* (* 2.0 i) (* 2.0 i)) 1.0))
81.0ms	(* i (/ 1 (- (* (* 2.0 i) (* 2.0 i)) 1.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	355	408
1	1450	397
2	5002	392

prune95.0ms

Filtered

67 candidates to 37 candidates (55.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	67	2	69

Merged error: 0b

Counts

69 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 0.00390625 (/ 1 (pow i 4)) (fma 0.015625 (/ 1 (pow i 2)) 0.0625))
0.4b	(/ 1 (pow i 2))
0.5b	(/ 1 (pow i 4))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-/r*`
2×	`pow-to-exp` `rec-exp` `pow-flip` `frac-2neg` `clear-num` `div-inv` `inv-pow` `sqr-pow`
1×	`fma-udef` `unpow2`

Counts

3 → 16

Calls

3 calls:

1.0ms	(fma 0.00390625 (/ 1 (pow i 4)) (fma 0.015625 (/ 1 (pow i 2)) 0.0625))
3.0ms	(/ 1 (pow i 2))
3.0ms	(/ 1 (pow i 4))

series79.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(fma 0.00390625 (/ 1 (pow i 4)) (fma 0.015625 (/ 1 (pow i 2)) 0.0625))
21.0ms	(/ 1 (pow i 2))
27.0ms	(/ 1 (pow i 4))

simplify50.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	65	57
1	188	56
2	1072	56
3	5003	56

prune45.0ms

Filtered

25 candidates to 14 candidates (56.0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	25	2	27

Merged error: 0b

Counts

27 → 2

regimes14.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.3b

bsearch43.0ms

Steps

Iters	Range		Point
8	10.915869392446634	14082.32902474981	245.0973832573261

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	31	15

end0.0ms

sample394.0ms

Algorithm

intervals

Results

226.0ms	8000×	body	80	valid
72.0ms	8000×	pre	80	true