Details

sample263.0ms

Algorithm

intervals

Results

80.0ms	98×	body	1280	valid
29.0ms	53×	body	640	valid
29.0ms	23×	body	640	nan
27.0ms	33×	body	10240	exit
17.0ms	173×	body	80	valid
14.0ms	12×	body	1280	nan
13.0ms	178×	body	80	nan
8.0ms	19×	body	320	valid
6.0ms	17×	body	320	nan
2.0ms	9×	body	160	nan
2.0ms	8×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1264
4	252
3	86
2	35
1	17
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite136.0ms

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:

7.0ms	(pow x (/ 1.0 n))
9.0ms	(pow (+ x 1.0) (/ 1.0 n))
110.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series697.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(pow x (/ 1.0 n))
230.0ms	(pow (+ x 1.0) (/ 1.0 n))
388.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.5s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	2866
1	738
0	270

prune636.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.2b

localize73.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
2.6b	(fma (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (- (pow (cbrt x) (/ 1.0 n))) (pow (cbrt (pow (+ x 1.0) (/ 1.0 n))) 3))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
0.0ms	(fma (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (- (pow (cbrt x) (/ 1.0 n))) (pow (cbrt (pow (+ x 1.0) (/ 1.0 n))) 3))

series1.6s

Counts

4 → 12

Calls

4 calls:

316.0ms	(cbrt x)
277.0ms	(cbrt x)
274.0ms	(cbrt x)
754.0ms	(fma (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (- (pow (cbrt x) (/ 1.0 n))) (pow (cbrt (pow (+ x 1.0) (/ 1.0 n))) 3))

simplify985.0ms

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
2	1664
1	398
0	147

prune679.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.1b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite384.0ms

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:

6.0ms	(pow x (/ 1.0 n))
16.0ms	(pow (+ x 1.0) (/ 1.0 n))
152.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
184.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

92.0ms	(pow x (/ 1.0 n))
225.0ms	(pow (+ x 1.0) (/ 1.0 n))
440.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
409.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify1.6s

Counts

249 → 249

Iterations

Iter	Nodes
done	5000
2	3211
1	927
0	429

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 19.9b

localize45.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.2b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.2b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

256×	`unpow-prod-down`
224×	`prod-diff`
222×	`*-un-lft-identity`
182×	`add-sqr-sqrt`
134×	`add-cube-cbrt`
128×	`log-prod`
122×	`sqrt-prod`
116×	`exp-sum`
86×	`sqr-pow`
36×	`log-pow` `difference-of-squares`
34×	`distribute-lft-out`
32×	`sqrt-pow1`
30×	`exp-prod`
16×	`fma-neg`
12×	`distribute-lft-out--`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 366

Calls

4 calls:

119.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
128.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
197.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
649.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series2.2s

Counts

4 → 12

Calls

4 calls:

384.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
448.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
688.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
691.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify1.5s

Counts

378 → 378

Iterations

Iter	Nodes
done	5002
2	2015
1	728
0	427

prune2.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 19.9b

regimes663.0ms

Accuracy

80.1% (1.8b remaining)

Error of 22.2b against oracle of 20.4b and baseline of 29.3b

bsearch2.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	38
2	38
1	36
0	33

end0.0ms

sample8.5s

Algorithm

intervals

Results

2.9s	3148×	body	1280	valid
1.1s	1592×	body	640	valid
965.0ms	1102×	body	10240	exit
925.0ms	672×	body	1280	nan
459.0ms	4688×	body	80	valid
397.0ms	864×	body	320	valid
369.0ms	5119×	body	80	nan
347.0ms	656×	body	640	nan
171.0ms	360×	body	320	nan
94.0ms	428×	body	160	valid
35.0ms	191×	body	160	nan