Details

sample132.0ms

Algorithm

intervals

Results

46.0ms	95×	body	1280	valid
15.0ms	42×	body	640	valid
14.0ms	33×	body	10240	exit
10.0ms	20×	body	1280	nan
7.0ms	143×	body	80	valid
7.0ms	19×	body	640	nan
6.0ms	170×	body	80	nan
6.0ms	25×	body	320	valid
3.0ms	13×	body	320	nan
2.0ms	18×	body	160	valid
1.0ms	5×	body	160	nan

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	35	13
3	86	13
4	228	13
5	743	13
6	3310	13
done	5000	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize8.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite67.0ms

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:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
53.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series487.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(pow x (/ 1.0 n))
149.0ms	(pow (+ x 1.0) (/ 1.0 n))
276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify795.0ms

Counts

158 → 158

Iterations

Useful iterations: done (790.0ms)

Iter	Nodes	Cost
0	271	4785
1	648	3566
2	1718	3220
done	5001	3079

prune333.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.7b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow x (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))
3.1b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite179.0ms

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:

2.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
105.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
53.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series960.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow x (/ 1.0 n))
155.0ms	(pow (+ x 1.0) (/ 1.0 n))
276.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
470.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify868.0ms

Counts

249 → 249

Iterations

Useful iterations: done (858.0ms)

Iter	Nodes	Cost
0	430	9019
1	827	6371
2	1965	5670
done	5000	5408

prune544.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.7b

localize16.0ms

Local error

Found 4 expressions with local error:

3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.1b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
3.1b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite228.0ms

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:

52.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
51.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
50.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
52.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

292.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
287.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
467.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
472.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify2.3s

Counts

346 → 346

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	401	16714
1	658	12152
2	1429	10744
3	4944	8780
done	5000	8780

prune972.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.6b

localize19.0ms

Local error

Found 4 expressions with local error:

1.7b	(pow (+ x 1.0) (/ 1.0 n))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.1b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

188×	`unpow-prod-down`
170×	`*-un-lft-identity`
168×	`prod-diff`
132×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
64×	`log-prod`
61×	`cbrt-prod`
60×	`sqr-pow`
58×	`exp-sum`
26×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
13×	`pow-unpow`
9×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg`
2×	`flip3--` `diff-log` `log-pow` `flip--`
1×	`pow-to-exp` `log-div` `cbrt-div` `pow-pow` `exp-diff` `pow1/3` `rem-log-exp` `pow-exp` `div-inv`

Counts

4 → 287

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
52.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
51.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
51.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

158.0ms	(pow (+ x 1.0) (/ 1.0 n))
298.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
295.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
484.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify856.0ms

Counts

299 → 299

Iterations

Useful iterations: done (842.0ms)

Iter	Nodes	Cost
0	450	12819
1	788	9351
2	1768	8303
done	5000	7891

prune802.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.6b

regimes276.0ms

Accuracy

79.5% (1.7b remaining)

Error of 23.0b against oracle of 21.3b and baseline of 29.7b

bsearch214.0ms

Steps

Iters	Range		Point
11	1.316736141892985e-13	3568380.5266111037	142153.58580214932
7	-6.957256490440221e+20	-4.3263376605350497e+18	-4.3921114290106465e+18

simplify11.0ms

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	37	90
1	50	68
done	50	68

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	3173×	body	1280	valid
544.0ms	1552×	body	640	valid
479.0ms	1149×	body	10240	exit
289.0ms	620×	body	1280	nan
247.0ms	4667×	body	80	valid
220.0ms	653×	body	640	nan
196.0ms	828×	body	320	valid
191.0ms	5001×	body	80	nan
72.0ms	374×	body	320	nan
63.0ms	461×	body	160	valid
20.0ms	173×	body	160	nan