Details

sample4.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.359131%

Guaranteed chance to sample good point: 62.745571%

Results

80.0ms	139×	body	1280	valid
32.0ms	29×	body	1280	nan
22.0ms	27×	body	640	nan
15.0ms	32×	body	640	valid
7.0ms	21×	body	320	valid
6.0ms	14×	body	320	nan
5.0ms	8×	body	640	invalid
4.0ms	50×	body	80	valid
3.0ms	3×	body	1280	invalid
3.0ms	14×	body	160	valid
2.0ms	7×	body	160	nan
1.0ms	3×	body	320	invalid
1.0ms	6×	body	80	invalid
0.0ms	2×	body	80	overflowed
0.0ms	1×	body	160	invalid
0.0ms	5×	body	80	nan

simplify34.0ms

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: 30.8b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
2.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite21.0ms

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:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
4.0ms	(pow x (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series74.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(pow (+ x 1.0) (/ 1.0 n))
15.0ms	(pow x (/ 1.0 n))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

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

prune180.0ms

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: 22.5b

Counts

89 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
0.0b	(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
2.8b	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

59×	`unpow-prod-down`
58×	`add-sqr-sqrt`
46×	`cbrt-prod`
32×	`*-un-lft-identity`
27×	`difference-of-squares`
25×	`cube-prod` `sqr-pow`
22×	`add-cube-cbrt`
16×	`pow-unpow`
9×	`times-frac`
7×	`add-exp-log`
6×	`add-log-exp`
5×	`pow1` `pow-exp` `add-cbrt-cube`
4×	`distribute-lft-out`
3×	`pow-to-exp`
2×	`cube-mult` `pow-pow` `unpow3`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `rem-cbrt-cube` `div-inv` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 133

Calls

4 calls:

3.0ms	(pow x (/ 1.0 n))
6.0ms	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
6.0ms	(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
18.0ms	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

series111.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow x (/ 1.0 n))
18.0ms	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
39.0ms	(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
41.0ms	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

simplify76.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	711	1354
1	2636	1299
2	5002	1282

prune233.0ms

Filtered

86 candidates to 145 candidates (-68.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	144	6	150

Merged error: 22.4b

Counts

150 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (* 2 (/ 1.0 n)))
0.0b	(pow x (* 2 (/ 1.0 n)))
0.3b	(/ (- (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n)))) (+ (pow x (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n))))
2.7b	(- (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

199×	`*-un-lft-identity`
151×	`unpow-prod-down`
125×	`add-sqr-sqrt`
90×	`times-frac`
73×	`distribute-lft-out`
72×	`difference-of-squares`
50×	`sqr-pow`
29×	`add-cube-cbrt`
24×	`distribute-lft-out--`
15×	`associate-/l*`
8×	`add-exp-log`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `pow-unpow` `flip3--` `pow-pow` `pow-exp` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 183

Calls

4 calls:

4.0ms	(pow (+ x 1.0) (* 2 (/ 1.0 n)))
2.0ms	(pow x (* 2 (/ 1.0 n)))
22.0ms	(/ (- (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n)))) (+ (pow x (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n))))
9.0ms	(- (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (+ x 1.0) (* 2 (/ 1.0 n)))
12.0ms	(pow x (* 2 (/ 1.0 n)))
246.0ms	(/ (- (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n)))) (+ (pow x (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n))))
38.0ms	(- (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n))))

simplify95.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	841	4019
1	3146	3890
2	5001	3864

prune520.0ms

Filtered

118 candidates to 195 candidates (-65.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	189	6	195
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	191	10	201

Merged error: 22.3b

Counts

201 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (pow x (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n))) (+ (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n)))))
0.0b	(* (pow x (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n))))
0.3b	(/ (- (* (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow (+ x 1.0) (* 2 (/ 1.0 n)))) (* (pow x (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n))))) (* (+ (pow x (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n))) (+ (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n))))))
2.7b	(- (* (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow (+ x 1.0) (* 2 (/ 1.0 n)))) (* (pow x (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n)))))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `*-un-lft-identity`
26×	`unpow-prod-down`
23×	`add-exp-log`
16×	`add-cube-cbrt`
13×	`associate-r` `associate-l` `add-cbrt-cube`
12×	`flip3-+` `flip-+`
11×	`prod-exp`
10×	`unswap-sqr` `sqr-pow`
8×	`frac-times` `associate-/r/` `distribute-lft-out`
7×	`swap-sqr`
6×	`pow1` `pow-to-exp` `pow-exp` `add-log-exp`
4×	`times-frac` `associate-r/` `associate-l/` `associate-/l*`
3×	`cbrt-unprod` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip--` `associate-/l/`
1×	`pow2` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `div-sub` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 133

Calls

4 calls:

21.0ms	(* (+ (pow x (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n))) (+ (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n)))))
7.0ms	(* (pow x (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n))))
31.0ms	(/ (- (* (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow (+ x 1.0) (* 2 (/ 1.0 n)))) (* (pow x (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n))))) (* (+ (pow x (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n))) (+ (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n))))))
10.0ms	(- (* (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow (+ x 1.0) (* 2 (/ 1.0 n)))) (* (pow x (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n)))))

series2.0s

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (+ (pow x (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n))) (+ (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n)))))
16.0ms	(* (pow x (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n))))
1.9s	(/ (- (* (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow (+ x 1.0) (* 2 (/ 1.0 n)))) (* (pow x (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n))))) (* (+ (pow x (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n))) (+ (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n))))))
56.0ms	(- (* (pow (+ x 1.0) (* 2 (/ 1.0 n))) (pow (+ x 1.0) (* 2 (/ 1.0 n)))) (* (pow x (* 2 (/ 1.0 n))) (pow x (* 2 (/ 1.0 n)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	999	3211
1	5002	2790

prune732.0ms

Filtered

103 candidates to 145 candidates (-40.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	138	7	145
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	143	12	155

Merged error: 22.3b

Counts

155 → 12

regimes410.0ms

Accuracy

84.3% (1.7b remaining)

Error of 23.5b against oracle of 21.7b and baseline of 32.7b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	97
1	64	97

end0.0ms

sample10.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.359131%

Guaranteed chance to sample good point: 62.745571%

Results

2.1s	3871×	body	1280	valid
1.1s	1026×	body	1280	nan
664.0ms	1491×	body	640	valid
603.0ms	875×	body	640	nan
221.0ms	713×	body	320	valid
185.0ms	426×	body	320	nan
167.0ms	240×	body	640	invalid
149.0ms	117×	body	1280	invalid
146.0ms	1606×	body	80	valid
78.0ms	183×	body	320	invalid
61.0ms	319×	body	160	valid
53.0ms	236×	body	160	nan
17.0ms	287×	body	80	nan
16.0ms	66×	body	160	invalid
16.0ms	127×	body	80	invalid
9.0ms	56×	body	80	overflowed

Details

sample4.3s

simplify34.0ms

prune3.0ms

localize9.0ms

rewrite21.0ms

series74.0ms

simplify49.0ms

prune180.0ms

localize13.0ms

rewrite38.0ms

series111.0ms

simplify76.0ms

prune233.0ms

localize16.0ms

rewrite51.0ms

series314.0ms

simplify95.0ms

prune520.0ms

localize23.0ms

rewrite277.0ms

series2.0s

simplify55.0ms

prune732.0ms

regimes410.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample10.3s

Profiling