Details

sample125.0ms

Algorithm

intervals

Results

39.0ms	89×	body	1280	valid
16.0ms	52×	body	640	valid
11.0ms	39×	body	10240	exit
8.0ms	168×	body	80	valid
7.0ms	25×	body	640	nan
6.0ms	184×	body	80	nan
6.0ms	28×	body	320	valid
5.0ms	14×	body	1280	nan
3.0ms	13×	body	320	nan
1.0ms	10×	body	160	valid
1.0ms	6×	body	160	nan

simplify35.0ms

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
done	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.8b

localize9.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 149

Calls

3 calls:

4.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
101.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series487.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(pow x (/ 1.0 n))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))
278.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify70.0ms

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	654	2164
1	2164	1642
2	5002	1637
done	5002	1637

prune336.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.0b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

202×	`unpow-prod-down`
179×	`*-un-lft-identity`
168×	`prod-diff`
144×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
67×	`sqr-pow`
28×	`distribute-lft-out`
27×	`difference-of-squares`
24×	`fma-neg`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 300

Calls

4 calls:

11.0ms	(pow (+ x 1.0) (/ 1.0 n))
96.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
97.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
99.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.0s

Counts

4 → 12

Calls

4 calls:

157.0ms	(pow (+ x 1.0) (/ 1.0 n))
287.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
283.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
280.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify83.0ms

Counts

312 → 312

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	542	5691
1	1694	4129
2	5001	4126
done	5001	4126

prune775.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
1.0b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

108×	`unpow-prod-down`
94×	`*-un-lft-identity`
91×	`add-sqr-sqrt`
56×	`prod-diff`
55×	`add-cube-cbrt`
37×	`sqr-pow`
36×	`cbrt-prod`
27×	`difference-of-squares`
26×	`pow-unpow`
18×	`times-frac`
15×	`cube-prod`
12×	`distribute-lft-out`
9×	`distribute-lft-out--`
8×	`fma-neg`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`cube-div` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 198

Calls

4 calls:

76.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
4.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
98.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series793.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
64.0ms	(pow x (/ 1.0 n))
150.0ms	(pow (+ x 1.0) (/ 1.0 n))
289.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify87.0ms

Counts

210 → 210

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	866	2811
1	3219	2300
2	5002	2294
done	5002	2294

prune499.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 17.0b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

202×	`unpow-prod-down`
179×	`*-un-lft-identity`
168×	`prod-diff`
144×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
67×	`sqr-pow`
28×	`distribute-lft-out`
27×	`difference-of-squares`
24×	`fma-neg`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 300

Calls

4 calls:

11.0ms	(pow (+ x 1.0) (/ 1.0 n))
96.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
95.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
99.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.0s

Counts

4 → 12

Calls

4 calls:

158.0ms	(pow (+ x 1.0) (/ 1.0 n))
286.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
291.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
292.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify87.0ms

Counts

312 → 312

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	542	5691
1	1694	4129
2	5001	4126
done	5001	4126

prune919.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 17.0b

regimes254.0ms

Accuracy

84.8% (1.3b remaining)

Error of 22.0b against oracle of 20.7b and baseline of 29.4b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	47
1	45	47
done	45	47

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.4s	3148×	body	1280	valid
541.0ms	1589×	body	640	valid
475.0ms	1200×	body	10240	exit
459.0ms	4796×	body	80	valid
290.0ms	668×	body	1280	nan
201.0ms	646×	body	640	nan
190.0ms	5148×	body	80	nan
185.0ms	844×	body	320	valid
65.0ms	442×	body	160	valid
65.0ms	346×	body	320	nan
19.0ms	176×	body	160	nan