Details

sample3.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 24.804688%

Guaranteed chance to sample good point: 65.974026%

Results

72.0ms	134×	body	1280	valid
38.0ms	34×	body	1280	nan
30.0ms	59×	body	640	valid
26.0ms	149×	body	80	overflowed
20.0ms	29×	body	640	nan
11.0ms	99×	body	80	valid
11.0ms	31×	body	320	valid
8.0ms	19×	body	320	nan
3.0ms	12×	body	160	valid
2.0ms	8×	body	160	nan
1.0ms	21×	body	80	nan

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	5001	6

prune3.0ms

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: 33.5b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.1b	(pow x (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
8.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series72.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(pow x (/ 1.0 n))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify51.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	552	688
1	1885	669
2	5002	641

prune196.0ms

Filtered

71 candidates to 88 candidates (-23.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 24.5b

Counts

89 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(exp (* (log x) (/ 1.0 n)))
0.4b	(* (log x) (/ 1.0 n))
3.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`times-frac`
13×	`pow-unpow` `associate-r`
10×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`add-log-exp`
5×	`unpow-prod-down`
4×	`associate-l`
3×	`difference-of-squares`
2×	`prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `pow-pow` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `pow-exp` `log-pow` `-commutative` `flip--` `rem-exp-log` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 87

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
2.0ms	(exp (* (log x) (/ 1.0 n)))
7.0ms	(* (log x) (/ 1.0 n))
7.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(exp (* (log x) (/ 1.0 n)))
12.0ms	(* (log x) (/ 1.0 n))
37.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

simplify60.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	615	749
1	2512	697
2	5002	683

prune174.0ms

Filtered

74 candidates to 99 candidates (-33.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	97	7	104

Merged error: 24.5b

Counts

104 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.0b	(* (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt (+ x 1.0)) (/ 1.0 n)))
0.1b	(pow x (/ 1.0 n))
3.0b	(- (* (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt` `unpow-prod-down`
49×	`*-un-lft-identity`
34×	`sqrt-prod`
33×	`add-cube-cbrt`
26×	`pow-unpow`
18×	`add-exp-log` `times-frac`
16×	`unswap-sqr`
15×	`swap-sqr` `sqr-pow`
11×	`associate-r` `associate-l`
9×	`prod-exp`
8×	`pow-to-exp` `pow-exp`
7×	`pow1` `distribute-lft-out`
6×	`add-cbrt-cube` `add-log-exp`
4×	`pow-pow`
3×	`difference-of-squares`
2×	`div-inv`
1×	`pow2` `sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-pow2` `flip--` `cbrt-unprod`

Counts

4 → 151

Calls

4 calls:

6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
13.0ms	(* (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt (+ x 1.0)) (/ 1.0 n)))
3.0ms	(pow x (/ 1.0 n))
14.0ms	(- (* (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

series168.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
53.0ms	(* (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt (+ x 1.0)) (/ 1.0 n)))
12.0ms	(pow x (/ 1.0 n))
73.0ms	(- (* (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

simplify76.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	681	1607
1	2754	1474
2	5001	1450

prune329.0ms

Filtered

101 candidates to 163 candidates (-61.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	163	7	170

Merged error: 24.5b

Counts

170 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

3.0b	(+ (- (- (* (/ 0 (pow n 2)) (/ 1.0 x)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2))))) (* 0.5 (/ 1 (* (pow x 2) n)))) (/ (/ 1.0 n) x))
5.2b	(/ 0 (pow n 2))
9.7b	(* (pow x 2) n)
10.1b	(* x (pow n 2))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
24×	`times-frac`
20×	`unpow-prod-down`
19×	`add-exp-log`
16×	`frac-sub`
13×	`associate-*r/` `add-log-exp`
12×	`frac-add`
11×	`associate-r` `associate-l`
10×	`add-cbrt-cube`
8×	`associate-/r*` `unpow2` `unswap-sqr` `sqr-pow`
6×	`prod-exp`
5×	`un-div-inv`
4×	`pow1` `associate-+l+`
3×	`pow-to-exp` `flip3--` `diff-log` `div-exp` `pow-exp` `sum-log` `flip--` `associate-/l*`
2×	`frac-times` `sub-neg` `associate-l/` `associate--l+` `-commutative` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `flip3-+` `div0` `clear-num` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 135

Calls

4 calls:

24.0ms	(+ (- (- (* (/ 0 (pow n 2)) (/ 1.0 x)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2))))) (* 0.5 (/ 1 (* (pow x 2) n)))) (/ (/ 1.0 n) x))
4.0ms	(/ 0 (pow n 2))
5.0ms	(* (pow x 2) n)
5.0ms	(* x (pow n 2))

series26.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (- (- (* (/ 0 (pow n 2)) (/ 1.0 x)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2))))) (* 0.5 (/ 1 (* (pow x 2) n)))) (/ (/ 1.0 n) x))
1.0ms	(/ 0 (pow n 2))
4.0ms	(* (pow x 2) n)
6.0ms	(* x (pow n 2))

simplify450.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	886	1712
1	4996	1392
2	5002	1392

prune307.0ms

Filtered

84 candidates to 147 candidates (-75.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	139	8	147
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	141	13	154

Merged error: 24.3b

Counts

154 → 13

regimes366.0ms

Accuracy

80.8% (2.1b remaining)

Error of 24.1b against oracle of 22.0b and baseline of 32.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	47
1	59	47

end0.0ms

sample10.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 24.804688%

Guaranteed chance to sample good point: 65.974026%

Results

2.2s	3906×	body	1280	valid
1.2s	1095×	body	1280	nan
893.0ms	1818×	body	640	valid
646.0ms	913×	body	640	nan
641.0ms	4159×	body	80	overflowed
338.0ms	3158×	body	80	valid
304.0ms	921×	body	320	valid
209.0ms	450×	body	320	nan
88.0ms	431×	body	160	valid
52.0ms	213×	body	160	nan
30.0ms	467×	body	80	nan

Details

sample3.3s

simplify36.0ms

prune3.0ms

localize9.0ms

rewrite19.0ms

series72.0ms

simplify51.0ms

prune196.0ms

localize11.0ms

rewrite22.0ms

series78.0ms

simplify60.0ms

prune174.0ms

localize11.0ms

rewrite41.0ms

series168.0ms

simplify76.0ms

prune329.0ms

localize24.0ms

rewrite43.0ms

series26.0ms

simplify450.0ms

prune307.0ms

regimes366.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample10.5s

Profiling