Details

sample145.0ms

Algorithm

intervals

Results

47.0ms	104×	body	1280	valid
22.0ms	34×	body	10240	exit
16.0ms	47×	body	640	valid
11.0ms	19×	body	1280	nan
8.0ms	153×	body	80	valid
6.0ms	28×	body	320	valid
5.0ms	139×	body	80	nan
4.0ms	17×	body	640	nan
3.0ms	18×	body	320	nan
2.0ms	16×	body	160	valid
1.0ms	7×	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: 28.3b

localize8.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.3b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite119.0ms

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))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
98.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series472.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(pow x (/ 1.0 n))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))
268.0ms	(- (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

prune331.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
1.0b	(pow x (/ 1.0 n))
1.3b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite196.0ms

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:

75.0ms	(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))
97.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series763.0ms

Counts

4 → 12

Calls

4 calls:

280.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
58.0ms	(pow x (/ 1.0 n))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))
276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify91.0ms

Counts

210 → 210

Iterations

Useful iterations: 2 (61.0ms)

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

prune480.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.3b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.3b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 237

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
94.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
182.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series775.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow x (/ 1.0 n))
153.0ms	(pow (+ x 1.0) (/ 1.0 n))
284.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
274.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify82.0ms

Counts

249 → 249

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	835	3935
1	2477	2885
2	5001	2880
done	5001	2880

prune532.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.3b

localize19.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.3b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

236×	`unpow-prod-down`
224×	`prod-diff`
206×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
128×	`log-prod`
122×	`cbrt-prod`
116×	`exp-sum`
74×	`sqr-pow`
32×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `sub-neg` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 334

Calls

4 calls:

92.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
92.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
80.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
82.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
460.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
460.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify92.0ms

Counts

346 → 346

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	665	7966
1	1642	6298
2	5001	5480
done	5001	5480

prune906.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.2b

regimes314.0ms

Accuracy

78% (1.8b remaining)

Error of 22.6b against oracle of 20.7b and baseline of 29.1b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	56
1	50	56
done	50	56

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3205×	body	1280	valid
539.0ms	1587×	body	640	valid
428.0ms	1158×	body	10240	exit
277.0ms	635×	body	1280	nan
238.0ms	4609×	body	80	valid
209.0ms	660×	body	640	nan
197.0ms	845×	body	320	valid
173.0ms	4864×	body	80	nan
69.0ms	359×	body	320	nan
57.0ms	421×	body	160	valid
21.0ms	199×	body	160	nan