Details

sample243.0ms

Algorithm

intervals

Results

64.0ms	113×	body	1280	valid
44.0ms	36×	body	1280	nan
30.0ms	68×	body	640	valid
23.0ms	151×	body	80	overflowed
16.0ms	22×	body	640	nan
12.0ms	223×	body	80	nan
11.0ms	107×	body	80	valid
10.0ms	34×	body	320	valid
7.0ms	17×	body	320	nan
2.0ms	9×	body	160	valid
1.0ms	4×	body	160	nan

simplify38.0ms

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

prune3.0ms

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: 35.9b

Counts

2 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

66×	`unpow-prod-down`
56×	`*-un-lft-identity` `prod-diff`
45×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
22×	`sqr-pow`
9×	`distribute-lft-out` `difference-of-squares`
8×	`fma-neg`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 90

Calls

1 calls:

11.0ms

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

series282.0ms

Counts

1 → 3

Calls

1 calls:

282.0ms

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

simplify52.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	413	1840
1	1182	1320
2	5002	1316

prune156.0ms

Filtered

93 candidates to 44 candidates (47.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Merged error: 24.4b

Counts

94 → 4

localize21.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
4.6b	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

102×	`unpow-prod-down`
80×	`prod-diff`
72×	`*-un-lft-identity`
65×	`add-sqr-sqrt`
48×	`add-cube-cbrt`
27×	`sqrt-prod`
26×	`sqr-pow`
12×	`difference-of-squares`
11×	`distribute-lft-out`
8×	`fma-neg`
4×	`add-log-exp`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `distribute-lft-out--`

Counts

2 → 125

Calls

2 calls:

13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.0ms	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

series1.5s

Counts

2 → 6

Calls

2 calls:

446.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.1s	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

simplify76.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	621	3815
1	1961	2692
2	5002	2656

prune286.0ms

Filtered

131 candidates to 59 candidates (45.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	131	4	135

Merged error: 24.4b

Counts

135 → 4

localize20.0ms

Local error

Found 3 expressions with local error:

1.6b

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

1.8b

(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))))

4.6b

(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

200×	`unpow-prod-down`
160×	`prod-diff`
141×	`*-un-lft-identity`
129×	`add-sqr-sqrt`
95×	`add-cube-cbrt`
85×	`log-prod`
82×	`exp-sum`
54×	`sqrt-prod`
51×	`sqr-pow`
24×	`difference-of-squares`
21×	`distribute-lft-out`
17×	`log-pow`
16×	`exp-prod`
8×	`fma-neg`
5×	`add-log-exp`
4×	`pow1`
3×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--` `fma-udef`

Counts

3 → 238

Calls

3 calls:

13.0ms

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

20.0ms

(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))))

1.0ms

(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

series2.0s

Counts

3 → 9

Calls

3 calls:

448.0ms

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

448.0ms

(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))))

1.1s

(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

simplify106.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	833	7303
1	2317	5082
2	5002	4358

prune529.0ms

Filtered

247 candidates to 103 candidates (41.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	246	5	251

Merged error: 24.4b

Counts

251 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.9b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n)))))))
1.9b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n)))))))
4.6b	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

278×	`unpow-prod-down`
240×	`prod-diff`
206×	`*-un-lft-identity`
176×	`log-prod`
170×	`cbrt-prod`
164×	`exp-sum`
159×	`add-sqr-sqrt`
142×	`add-cube-cbrt`
75×	`sqrt-prod`
62×	`sqr-pow`
31×	`distribute-lft-out`
12×	`difference-of-squares`
8×	`fma-neg`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg`
2×	`log-div` `cbrt-div` `exp-diff` `pow1/3` `rem-log-exp`
1×	`flip3--` `diff-log` `flip--` `fma-udef` `distribute-lft-out--`

Counts

4 → 327

Calls

4 calls:

13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
22.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n)))))))
25.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n)))))))
1.0ms	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

series4.0s

Counts

4 → 12

Calls

4 calls:

443.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
1.1s	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n)))))))
1.3s	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n)))))))
1.1s	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

simplify155.0ms

Algorithm

egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	965	11743
1	2632	9511
2	5001	8138

prune957.0ms

Filtered

339 candidates to 129 candidates (38.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	336	3	339
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	337	7	344

Merged error: 24.3b

Counts

344 → 7

regimes219.0ms

Accuracy

84.1% (1.7b remaining)

Error of 24.1b against oracle of 22.4b and baseline of 33.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	80
1	59	80

end0.0ms

sample7.4s

Algorithm

intervals

Results

2.2s	3942×	body	1280	valid
1.3s	1081×	body	1280	nan
832.0ms	1778×	body	640	valid
678.0ms	926×	body	640	nan
659.0ms	4101×	body	80	overflowed
338.0ms	3101×	body	80	valid
309.0ms	6210×	body	80	nan
293.0ms	889×	body	320	valid
188.0ms	434×	body	320	nan
89.0ms	450×	body	160	valid
52.0ms	232×	body	160	nan

Details

sample243.0ms

simplify38.0ms

prune3.0ms

localize9.0ms

rewrite16.0ms

series282.0ms

simplify52.0ms

prune156.0ms

localize21.0ms

rewrite21.0ms

series1.5s

simplify76.0ms

prune286.0ms

localize20.0ms

rewrite53.0ms

series2.0s

simplify106.0ms

prune529.0ms

localize24.0ms

rewrite91.0ms

series4.0s

simplify155.0ms

prune957.0ms

regimes219.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample7.4s

Profiling