Details

sample206.0ms

Algorithm

intervals

Results

66.0ms	133×	body	1280	valid
36.0ms	60×	body	1280	nan
22.0ms	51×	body	640	valid
20.0ms	50×	body	640	nan
14.0ms	28×	body	10240	exit
8.0ms	187×	body	80	nan
8.0ms	30×	body	320	nan
6.0ms	24×	body	320	valid
4.0ms	93×	body	80	valid
2.0ms	14×	body	160	nan
2.0ms	13×	body	160	valid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	35	6
2	85	6
3	249	6
4	911	6
5	5001	6

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: 32.4b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow x (/ 1.0 n))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-unpow` `flip3--` `fma-neg` `prod-diff` `flip--` `div-inv` `difference-of-squares`

Counts

2 → 10

Calls

2 calls:

2.0ms	(pow x (/ 1.0 n))
4.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series355.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(pow x (/ 1.0 n))
291.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify107.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	267	192
1	864	170
2	4257	158
3	5001	152

prune62.0ms

Filtered

16 candidates to 14 candidates (87.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	13	3	16
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	14	3	17

Merged error: 21.7b

Counts

17 → 3

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b

(+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

0.0b

(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))

1.9b

(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqr-pow`
4×	`frac-times` `flip3--` `flip3-+` `flip--` `flip-+`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `prod-diff`
2×	`associate-r/` `associate-l/` `difference-of-squares`
1×	`+-commutative` `fma-def` `fma-neg` `associate-r` `*-commutative`

Counts

3 → 27

Calls

3 calls:

8.0ms

(+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

10.0ms

(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))

5.0ms

(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series1.0s

Counts

3 → 9

Calls

3 calls:

220.0ms

(+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

515.0ms

(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))

295.0ms

(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify44.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	365	787
1	1342	762
2	5001	740

prune145.0ms

Filtered

36 candidates to 31 candidates (86.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	33	6	39

Merged error: 21.6b

Counts

39 → 6

localize35.0ms

Local error

Found 4 expressions with local error:

3.5b	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x)))
4.0b	(fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x))
7.5b	(* x (pow n 2))
9.4b	(* (pow x 2) n)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-commutative` `fma-udef`
2×	`associate-r` `associate-l` `associate-*l/` `unpow2` `sqr-pow`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x)))
1.0ms	(fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x))
3.0ms	(* x (pow n 2))
3.0ms	(* (pow x 2) n)

series545.0ms

Counts

4 → 12

Calls

4 calls:

399.0ms	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x)))
98.0ms	(fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x))
30.0ms	(* x (pow n 2))
18.0ms	(* (pow x 2) n)

simplify37.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	328	269
1	1324	265
2	5002	253

prune108.0ms

Filtered

24 candidates to 16 candidates (66.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	24	6	30

Merged error: 21.6b

Counts

30 → 6

localize37.0ms

Local error

Found 4 expressions with local error:

3.5b	(* (- (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))) (fma 0.25 (/ (log (/ 1 x)) (* x (pow n 2))) (/ (/ 0.25 n) (pow x 2))))
4.0b	(+ (* (- (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))) (fma 0.25 (/ (log (/ 1 x)) (* x (pow n 2))) (/ (/ 0.25 n) (pow x 2)))) (* (/ (/ 0.5 n) x) (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
7.5b	(* x (pow n 2))
8.9b	(/ (/ 0.25 n) (pow x 2))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

62×	`associate-*l/`
48×	`distribute-neg-frac`
46×	`frac-add`
41×	`flip3-+` `flip-+`
28×	`frac-times`
21×	`associate-/l/`
14×	`frac-2neg` `clear-num`
10×	`div-inv`
7×	`associate-/l*`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-*r/` `fma-udef`
3×	`+-commutative` `fma-def` `*-commutative` `unpow2` `sqr-pow`
2×	`neg-mul-1` `associate-+l+` `times-frac` `associate-r` `associate-l` `associate-/r*`
1×	`distribute-lft-neg-out`

Counts

4 → 79

Calls

4 calls:

6.0ms	(* (- (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))) (fma 0.25 (/ (log (/ 1 x)) (* x (pow n 2))) (/ (/ 0.25 n) (pow x 2))))
18.0ms	(+ (* (- (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))) (fma 0.25 (/ (log (/ 1 x)) (* x (pow n 2))) (/ (/ 0.25 n) (pow x 2)))) (* (/ (/ 0.5 n) x) (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
3.0ms	(* x (pow n 2))
4.0ms	(/ (/ 0.25 n) (pow x 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

527.0ms	(* (- (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))) (fma 0.25 (/ (log (/ 1 x)) (* x (pow n 2))) (/ (/ 0.25 n) (pow x 2))))
667.0ms	(+ (* (- (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))) (fma 0.25 (/ (log (/ 1 x)) (* x (pow n 2))) (/ (/ 0.25 n) (pow x 2)))) (* (/ (/ 0.5 n) x) (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
37.0ms	(* x (pow n 2))
26.0ms	(/ (/ 0.25 n) (pow x 2))

simplify73.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1284	4972
1	5002	4758

prune586.0ms

Filtered

91 candidates to 75 candidates (82.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	91	6	97

Merged error: 21.6b

Counts

97 → 6

regimes212.0ms

Accuracy

84.5% (1.6b remaining)

Error of 23.3b against oracle of 21.7b and baseline of 32.2b

bsearch2.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	181
1	82	181
2	83	181
3	83	181

end0.0ms

sample6.7s

Algorithm

intervals

Results

1.9s	3926×	body	1280	valid
1.4s	2181×	body	1280	nan
759.0ms	1799×	body	640	nan
625.0ms	1410×	body	10240	exit
608.0ms	1762×	body	640	valid
268.0ms	6260×	body	80	nan
227.0ms	868×	body	320	nan
195.0ms	861×	body	320	valid
165.0ms	3228×	body	80	valid
66.0ms	462×	body	160	valid
65.0ms	430×	body	160	nan