Details

sample4.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.076294%

Guaranteed chance to sample good point: 49.896135%

Results

72.0ms	128×	body	1280	valid
46.0ms	39×	body	1280	nan
21.0ms	46×	body	640	valid
19.0ms	129×	body	80	overflowed
17.0ms	23×	body	640	nan
8.0ms	27×	body	320	valid
7.0ms	59×	body	80	invalid
6.0ms	9×	body	640	invalid
5.0ms	11×	body	320	nan
4.0ms	43×	body	80	valid
3.0ms	8×	body	320	invalid
3.0ms	2×	body	1280	invalid
3.0ms	12×	body	160	valid
2.0ms	7×	body	160	nan
1.0ms	15×	body	80	nan
0.0ms	2×	body	160	invalid

simplify33.0ms

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: 33.3b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite26.0ms

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:

3.0ms	(pow x (/ 1.0 n))
9.0ms	(pow (+ x 1.0) (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series85.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(pow x (/ 1.0 n))
18.0ms	(pow (+ x 1.0) (/ 1.0 n))
55.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify48.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

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

prune198.0ms

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: 23.5b

Counts

89 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(log (exp (pow x (/ 1.0 n))))
0.0b	(exp (pow x (/ 1.0 n)))
2.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (log (exp (pow x (/ 1.0 n)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
14×	`exp-prod`
13×	`pow-unpow`
11×	`unpow-prod-down`
9×	`times-frac` `log-pow`
7×	`pow1`
6×	`log-prod` `add-log-exp`
5×	`add-exp-log`
4×	`add-cbrt-cube` `sqr-pow`
3×	`associate--r+` `difference-of-squares`
2×	`distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `rem-log-exp` `pow-exp` `flip--` `div-inv` `rem-exp-log` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
3.0ms	(log (exp (pow x (/ 1.0 n))))
3.0ms	(exp (pow x (/ 1.0 n)))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (log (exp (pow x (/ 1.0 n)))))

series87.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(log (exp (pow x (/ 1.0 n))))
16.0ms	(exp (pow x (/ 1.0 n)))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (log (exp (pow x (/ 1.0 n)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	657	771
1	2366	715
2	5002	698

prune228.0ms

Filtered

77 candidates to 94 candidates (-22.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	93	6	99

Merged error: 23.3b

Counts

99 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

4.5b	(+ (- (- (* (/ 1.0 x) (/ 0 (pow n 2))) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2))))) (* 0.5 (/ 1 (* (pow x 2) n)))) (/ (/ 1.0 n) x))
6.2b	(/ 0 (pow n 2))
8.5b	(* x (pow n 2))
8.8b	(* (pow x 2) n)

rewrite45.0ms

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`
18×	`frac-sub`
16×	`associate-*r/`
14×	`frac-add`
13×	`add-log-exp`
11×	`associate-r` `associate-l`
10×	`add-cbrt-cube`
8×	`associate-/r*` `unpow2` `unswap-sqr` `sqr-pow`
6×	`prod-exp` `un-div-inv`
4×	`pow1` `frac-times` `associate-+l+`
3×	`pow-to-exp` `flip3--` `diff-log` `div-exp` `pow-exp` `sum-log` `flip--` `associate-/l*`
2×	`sub-neg` `associate-l/` `associate--l+` `-commutative` `cbrt-unprod` `sub-div`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `flip3-+` `div0` `clear-num` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 137

Calls

4 calls:

25.0ms	(+ (- (- (* (/ 1.0 x) (/ 0 (pow n 2))) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2))))) (* 0.5 (/ 1 (* (pow x 2) n)))) (/ (/ 1.0 n) x))
5.0ms	(/ 0 (pow n 2))
5.0ms	(* x (pow n 2))
5.0ms	(* (pow x 2) n)

series37.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (- (- (* (/ 1.0 x) (/ 0 (pow n 2))) (* 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))
7.0ms	(* x (pow n 2))
4.0ms	(* (pow x 2) n)

simplify46.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	924	1766
1	5001	1447

prune371.0ms

Filtered

84 candidates to 149 candidates (-77.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	142	7	149
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	143	12	155

Merged error: 23.2b

Counts

155 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

4.5b	(+ (- (- (* (/ 1.0 x) (/ 0 (pow n 2))) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2))))) (* 0.5 (/ 1 (log (exp (* (pow x 2) n)))))) (/ (/ 1.0 n) x))
6.2b	(/ 0 (pow n 2))
8.5b	(* x (pow n 2))
8.8b	(* (pow x 2) n)

rewrite45.0ms

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`
18×	`frac-sub`
16×	`associate-*r/`
14×	`frac-add`
13×	`add-log-exp`
11×	`associate-r` `associate-l`
10×	`add-cbrt-cube`
8×	`associate-/r*` `unpow2` `unswap-sqr` `sqr-pow`
6×	`prod-exp` `un-div-inv`
4×	`pow1` `frac-times` `associate-+l+`
3×	`pow-to-exp` `flip3--` `diff-log` `div-exp` `pow-exp` `sum-log` `flip--` `associate-/l*`
2×	`sub-neg` `associate-l/` `associate--l+` `-commutative` `cbrt-unprod` `sub-div`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `flip3-+` `div0` `clear-num` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 137

Calls

4 calls:

24.0ms	(+ (- (- (* (/ 1.0 x) (/ 0 (pow n 2))) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2))))) (* 0.5 (/ 1 (log (exp (* (pow x 2) n)))))) (/ (/ 1.0 n) x))
5.0ms	(/ 0 (pow n 2))
5.0ms	(* x (pow n 2))
7.0ms	(* (pow x 2) n)

series30.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (- (- (* (/ 1.0 x) (/ 0 (pow n 2))) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2))))) (* 0.5 (/ 1 (log (exp (* (pow x 2) n)))))) (/ (/ 1.0 n) x))
1.0ms	(/ 0 (pow n 2))
6.0ms	(* x (pow n 2))
4.0ms	(* (pow x 2) n)

simplify47.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	906	1860
1	5001	1477

prune343.0ms

Filtered

83 candidates to 149 candidates (-79.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	148	13	161

Merged error: 23.2b

Counts

161 → 13

regimes416.0ms

Accuracy

88.8% (2.2b remaining)

Error of 23.5b against oracle of 21.3b and baseline of 41.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	57
1	66	57

end0.0ms

sample11.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.076294%

Guaranteed chance to sample good point: 49.896135%

Results

2.1s	3815×	body	1280	valid
1.3s	1150×	body	1280	nan
687.0ms	942×	body	640	nan
673.0ms	1494×	body	640	valid
643.0ms	4186×	body	80	overflowed
224.0ms	716×	body	320	valid
211.0ms	472×	body	320	nan
181.0ms	1446×	body	80	invalid
179.0ms	261×	body	640	invalid
146.0ms	109×	body	1280	invalid
144.0ms	1614×	body	80	valid
74.0ms	185×	body	320	invalid
71.0ms	361×	body	160	valid
50.0ms	206×	body	160	nan
30.0ms	475×	body	80	nan
20.0ms	82×	body	160	invalid

Details

sample4.5s

simplify33.0ms

prune3.0ms

localize9.0ms

rewrite26.0ms

series85.0ms

simplify48.0ms

prune198.0ms

localize12.0ms

rewrite26.0ms

series87.0ms

simplify56.0ms

prune228.0ms

localize25.0ms

rewrite45.0ms

series37.0ms

simplify46.0ms

prune371.0ms

localize25.0ms

rewrite45.0ms

series30.0ms

simplify47.0ms

prune343.0ms

regimes416.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample11.8s

Profiling