Details

sample52.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.520795%

Guaranteed chance to sample good point: 65.377249%

Results

15.0ms	51×	body	1280	valid
12.0ms	46×	body	640	valid
7.0ms	133×	body	80	valid
4.0ms	113×	body	80	nan
2.0ms	20×	body	320	valid
0.0ms	6×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

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: 29.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (log (+ N 1.0)) (log N))
4.5b	(log (+ N 1.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`pow1` `add-sqr-sqrt`
5×	`add-cube-cbrt` `log-pow`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

6.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

series9.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(- (log (+ N 1.0)) (log N))
4.0ms	(log (+ N 1.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	232	285
1	628	264
2	2171	244
3	5001	244

prune83.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	3	48

Merged error: 0.0b

Counts

48 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

4.5b	(log (+ N 1.0))
4.5b	(log (+ N 1.0))
4.5b	(log (+ N 1.0))
19.0b	(- (* (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0)))) (log N))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

15×	`log-prod`
14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`pow1` `add-exp-log`
6×	`log-div`
5×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`flip3-+` `rem-log-exp` `log-pow` `flip-+` `distribute-lft-out` `associate--r+`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 60

Calls

4 calls:

3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
9.0ms	(- (* (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0)))) (log N))

series14.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
6.0ms	(- (* (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0)))) (log N))

simplify63.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	237	617
1	676	492
2	2357	423
3	5003	414

prune152.0ms

Filtered

54 candidates to 72 candidates (-33.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	72	3	75

Merged error: 0.0b

Counts

75 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))))
19.6b	(log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))
21.5b	(- (- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))) (log N))
21.9b	(log (+ (pow N 3) (pow 1.0 3)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
36×	`log-prod`
31×	`associate--l+`
23×	`pow1`
22×	`distribute-lft-out--`
19×	`log-pow`
15×	`distribute-lft-out`
14×	`add-sqr-sqrt`
12×	`unpow-prod-down` `cube-prod`
10×	`add-cube-cbrt` `log-div`
6×	`add-exp-log` `associate--r+`
5×	`flip3-+` `flip-+` `add-log-exp`
4×	`diff-log` `add-cbrt-cube` `associate--r-`
3×	`associate--l-` `sub-neg` `sum-cubes`
2×	`flip3--` `rem-log-exp` `flip--` `difference-of-squares`

Counts

4 → 108

Calls

4 calls:

17.0ms	(- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))))
5.0ms	(log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))
21.0ms	(- (- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))) (log N))
10.0ms	(log (+ (pow N 3) (pow 1.0 3)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))))
4.0ms	(log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))
9.0ms	(- (- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))) (log N))
13.0ms	(log (+ (pow N 3) (pow 1.0 3)))

simplify58.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	524	1518
1	1908	1455
2	5002	1403

prune252.0ms

Filtered

82 candidates to 120 candidates (-46.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	120	3	123

Merged error: 0.0b

Counts

123 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.1b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.2b	(/ 1 (pow N 2))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
57×	`times-frac`
42×	`*-un-lft-identity`
36×	`add-cube-cbrt`
32×	`add-exp-log`
28×	`associate-l`
23×	`unpow-prod-down`
12×	`div-exp`
10×	`prod-exp` `add-cbrt-cube`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`associate-/r*`
6×	`pow-to-exp` `rec-exp` `1-exp` `associate-r` `pow-exp`
5×	`pow1` `frac-add` `add-log-exp`
4×	`distribute-rgt-in` `frac-times` `sub-neg` `associate-+l+` `flip3--` `distribute-lft-in` `associate-*r/` `flip--`
3×	`associate-/l*`
2×	`cbrt-undiv` `associate-*l/` `cbrt-unprod` `div-inv` `difference-of-squares`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip-+` `distribute-lft-out--` `inv-pow`

Counts

3 → 150

Calls

3 calls:

14.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
15.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 1 (pow N 2))

series12.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
6.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
2.0ms	(/ 1 (pow N 2))

simplify67.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	583	1115
1	2789	903
2	5001	840

prune164.0ms

Filtered

89 candidates to 159 candidates (-78.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	158	4	162

Merged error: 0b

Counts

162 → 4

regimes40.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.2b

bsearch16.0ms

Steps

Iters	Range		Point
9	0.05542000641073973	1164766.93919775	3232.7051255941346

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	20
1	29	20

end0.0ms

sample1.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.520795%

Guaranteed chance to sample good point: 65.377249%

Results

496.0ms	1730×	body	1280	valid
243.0ms	1309×	body	640	valid
200.0ms	4024×	body	80	valid
158.0ms	4147×	body	80	nan
79.0ms	626×	body	320	valid
24.0ms	311×	body	160	valid

Details

sample52.0ms

simplify4.0ms

prune2.0ms

localize6.0ms

rewrite10.0ms

series9.0ms

simplify56.0ms

prune83.0ms

localize10.0ms

rewrite19.0ms

series14.0ms

simplify63.0ms

prune152.0ms

localize17.0ms

rewrite56.0ms

series35.0ms

simplify58.0ms

prune252.0ms

localize9.0ms

rewrite41.0ms

series12.0ms

simplify67.0ms

prune164.0ms

regimes40.0ms

bsearch16.0ms

simplify1.0ms

end0.0ms

sample1.4s

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