Details

sample207.0ms

Algorithm

intervals

Results

58.0ms	91×	body	1280	valid
30.0ms	60×	body	640	valid
25.0ms	28×	body	10240	exit
15.0ms	22×	body	1280	nan
13.0ms	19×	body	640	nan
12.0ms	139×	body	80	valid
11.0ms	37×	body	320	valid
10.0ms	154×	body	80	nan
4.0ms	11×	body	320	nan
4.0ms	16×	body	160	valid
1.0ms	7×	body	160	nan

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
6	2902
5	690
4	225
3	81
2	34
1	17
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize29.0ms

Local error

Found 3 expressions with local error:

0.2b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

3.0ms	(pow x (/ 1.0 n))
9.0ms	(pow (+ x 1.0) (/ 1.0 n))
96.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series705.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(pow x (/ 1.0 n))
208.0ms	(pow (+ x 1.0) (/ 1.0 n))
420.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify3.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	4849
2	1452
1	530
0	189

prune568.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
3.7b	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
32×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
27×	`times-frac`
12×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube` `sqr-pow`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `difference-of-squares`
2×	`distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 98

Calls

4 calls:

6.0ms	(pow x (/ 1.0 n))
12.0ms	(pow (+ x 1.0) (/ 1.0 n))
9.0ms	(pow (+ x 1.0) (/ 1.0 n))
33.0ms	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

series946.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(pow x (/ 1.0 n))
235.0ms	(pow (+ x 1.0) (/ 1.0 n))
215.0ms	(pow (+ x 1.0) (/ 1.0 n))
397.0ms	(- (* (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

simplify2.9s

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
3	4755
2	1408
1	512
0	180

prune779.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 22.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log x) (/ 1.0 n))
1.0b	(pow (+ 1.0 x) (/ 1.0 n))
3.2b	(log (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))))
3.2b	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

rewrite310.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`times-frac`
13×	`pow-unpow` `associate-r`
10×	`add-exp-log`
9×	`pow1` `add-cbrt-cube` `log-pow`
7×	`exp-prod`
6×	`unpow-prod-down` `add-log-exp` `difference-of-squares`
5×	`log-prod`
4×	`associate-l`
3×	`sqr-pow`
2×	`sub-neg` `exp-sum` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`
1×	`pow-to-exp` `cbrt-undiv` `log-div` `pow-pow` `flip3--` `exp-diff` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `pow-exp` `associate-r/` `-commutative` `flip--` `distribute-lft-out`

Counts

4 → 99

Calls

4 calls:

17.0ms	(* (log x) (/ 1.0 n))
8.0ms	(pow (+ 1.0 x) (/ 1.0 n))
172.0ms	(log (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))))
107.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

series1.2s

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (log x) (/ 1.0 n))
196.0ms	(pow (+ 1.0 x) (/ 1.0 n))
409.0ms	(log (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))))
442.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

simplify1.7s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
2	1636
1	564
0	214

prune884.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 22.6b

localize38.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))
3.2b	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))
3.2b	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))))))
3.2b	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))))))

rewrite508.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
20×	`log-pow`
18×	`*-un-lft-identity`
16×	`log-prod` `sqrt-pow1`
14×	`exp-prod`
12×	`difference-of-squares`
10×	`add-cube-cbrt` `sqrt-prod`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`sub-neg` `unpow-prod-down` `add-cbrt-cube` `exp-sum` `distribute-lft-out--` `sqr-pow`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 86

Calls

4 calls:

76.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))
97.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))
154.0ms	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))))))
177.0ms	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))))))

series2.1s

Counts

4 → 12

Calls

4 calls:

417.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))
375.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))
583.0ms	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))))))
699.0ms	(log (sqrt (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))))))

simplify2.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
3	2526
2	763
1	302
0	139

prune750.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 22.6b

regimes697.0ms

Accuracy

81.9% (1.6b remaining)

Error of 22.4b against oracle of 20.7b and baseline of 29.8b

bsearch255.0ms

Steps

Iters	Range		Point
7	457080.382362169	12146952.384825662	9526334.64054044
8	-3.780967145050149e+24	-1.277026833780439e+21	-1.3035027251044724e+21

simplify7.0ms

Iterations

Iter	Nodes
done	43
1	43
0	37

end0.0ms

sample8.2s

Algorithm

intervals

Results

2.4s	3203×	body	1280	valid
1.4s	1578×	body	640	valid
937.0ms	4719×	body	80	valid
852.0ms	1181×	body	10240	exit
686.0ms	686×	body	1280	nan
364.0ms	606×	body	640	nan
345.0ms	861×	body	320	valid
344.0ms	5102×	body	80	nan
145.0ms	331×	body	320	nan
144.0ms	446×	body	160	valid
70.0ms	187×	body	160	nan