Details

sample233.0ms

Algorithm

intervals

Results

70.0ms	141×	body	1280	valid
36.0ms	62×	body	1280	nan
30.0ms	74×	body	640	nan
23.0ms	43×	body	10240	exit
18.0ms	55×	body	640	valid
10.0ms	216×	body	80	nan
9.0ms	33×	body	320	nan
6.0ms	118×	body	80	valid
5.0ms	20×	body	320	valid
2.0ms	14×	body	160	valid
2.0ms	12×	body	160	nan

simplify37.0ms

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

prune2.0ms

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: 31.3b

Counts

2 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

1.7b	(- (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)))

series277.0ms

Counts

1 → 3

Calls

1 calls:

277.0ms

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

simplify53.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (36.0ms)

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

prune144.0ms

Filtered

93 candidates to 44 candidates (47.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	3	94

Merged error: 20.8b

Counts

94 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
2.6b	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
1.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

series1.1s

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt (+ x 1.0))
89.0ms	(cbrt (+ x 1.0))
88.0ms	(cbrt (+ x 1.0))
856.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

simplify45.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	465	701
1	1620	644
2	5001	634

prune283.0ms

Filtered

70 candidates to 64 candidates (91.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	68	5	73

Merged error: 20.6b

Counts

73 → 5

localize46.0ms

Local error

Found 4 expressions with local error:

5.2b	(pow (/ 1 x) -1/3)
8.2b	(pow (fma (pow (/ 1 (pow x 2)) 1/3) 0.3333333333333333 (- (pow (/ 1 x) -1/3) (* 0.1111111111111111 (pow (/ 1 (pow x 5)) 1/3)))) (/ 1.0 n))
21.0b	(pow (/ 1 (pow x 5)) 1/3)
36.3b	(pow (/ 1 (pow x 2)) 1/3)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

87×	`unpow-prod-down`
63×	`times-frac`
51×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
31×	`pow-exp`
30×	`add-exp-log`
22×	`pow-unpow`
14×	`div-exp`
10×	`pow-to-exp` `pow-pow` `sqr-pow`
9×	`pow1`
7×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip` `unpow2` `inv-pow`
2×	`unpow1/3`

Counts

4 → 172

Calls

4 calls:

5.0ms	(pow (/ 1 x) -1/3)
4.0ms	(pow (fma (pow (/ 1 (pow x 2)) 1/3) 0.3333333333333333 (- (pow (/ 1 x) -1/3) (* 0.1111111111111111 (pow (/ 1 (pow x 5)) 1/3)))) (/ 1.0 n))
7.0ms	(pow (/ 1 (pow x 5)) 1/3)
8.0ms	(pow (/ 1 (pow x 2)) 1/3)

series828.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(pow (/ 1 x) -1/3)
276.0ms	(pow (fma (pow (/ 1 (pow x 2)) 1/3) 0.3333333333333333 (- (pow (/ 1 x) -1/3) (* 0.1111111111111111 (pow (/ 1 (pow x 5)) 1/3)))) (/ 1.0 n))
209.0ms	(pow (/ 1 (pow x 5)) 1/3)
173.0ms	(pow (/ 1 (pow x 2)) 1/3)

simplify87.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	1022	1370
1	3965	1196
2	5003	1187

prune628.0ms

Filtered

184 candidates to 89 candidates (48.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	182	2	184
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	183	6	189

Merged error: 20.6b

Counts

189 → 6

localize41.0ms

Local error

Found 4 expressions with local error:

5.2b	(pow (/ 1 x) -1/3)
6.1b	(pow x -2/3)
8.2b	(pow (fma (pow x -2/3) 0.3333333333333333 (- (pow (/ 1 x) -1/3) (* 0.1111111111111111 (pow (/ 1 (pow x 5)) 1/3)))) (/ 1.0 n))
21.0b	(pow (/ 1 (pow x 5)) 1/3)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

53×	`unpow-prod-down`
39×	`times-frac`
37×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`pow-unpow`
21×	`add-exp-log`
19×	`pow-exp`
9×	`pow1`
8×	`pow-pow` `div-exp`
7×	`pow-to-exp` `sqr-pow`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`pow-flip` `inv-pow`
1×	`unpow1/3`

Counts

4 → 135

Calls

4 calls:

5.0ms	(pow (/ 1 x) -1/3)
2.0ms	(pow x -2/3)
3.0ms	(pow (fma (pow x -2/3) 0.3333333333333333 (- (pow (/ 1 x) -1/3) (* 0.1111111111111111 (pow (/ 1 (pow x 5)) 1/3)))) (/ 1.0 n))
7.0ms	(pow (/ 1 (pow x 5)) 1/3)

series838.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(pow (/ 1 x) -1/3)
176.0ms	(pow x -2/3)
283.0ms	(pow (fma (pow x -2/3) 0.3333333333333333 (- (pow (/ 1 x) -1/3) (* 0.1111111111111111 (pow (/ 1 (pow x 5)) 1/3)))) (/ 1.0 n))
208.0ms	(pow (/ 1 (pow x 5)) 1/3)

simplify77.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	799	1027
1	3191	940
2	5001	934

prune520.0ms

Filtered

147 candidates to 83 candidates (56.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	148	5	153

Merged error: 20.6b

Counts

153 → 5

regimes179.0ms

Accuracy

79.3% (2.2b remaining)

Error of 24.6b against oracle of 22.4b and baseline of 33.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	31
1	45	31

end0.0ms

sample6.7s

Algorithm

intervals

Results

1.9s	3855×	body	1280	valid
1.3s	2106×	body	1280	nan
777.0ms	1845×	body	640	nan
651.0ms	1868×	body	640	valid
579.0ms	1385×	body	10240	exit
279.0ms	6163×	body	80	nan
245.0ms	924×	body	320	nan
203.0ms	898×	body	320	valid
156.0ms	3138×	body	80	valid
69.0ms	468×	body	160	nan
65.0ms	448×	body	160	valid