Details

sample240.0ms

Algorithm

intervals

Results

83.0ms	103×	body	1280	valid
25.0ms	29×	body	1280	nan
19.0ms	186×	body	80	valid
19.0ms	31×	body	640	valid
18.0ms	30×	body	10240	exit
12.0ms	30×	body	320	valid
12.0ms	16×	body	640	nan
12.0ms	164×	body	80	nan
4.0ms	10×	body	320	nan
2.0ms	11×	body	160	valid
2.0ms	7×	body	160	nan

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1231
4	238
3	81
2	34
1	17
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.4b

localize17.0ms

Local error

Found 3 expressions with local error:

0.7b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite100.0ms

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:

6.0ms	(pow x (/ 1.0 n))
15.0ms	(pow (+ x 1.0) (/ 1.0 n))
75.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series645.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(pow x (/ 1.0 n))
208.0ms	(pow (+ x 1.0) (/ 1.0 n))
362.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.5s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	2073
1	544
0	189

prune556.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
1.0b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite342.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
27×	`unpow-prod-down`
26×	`pow-unpow`
22×	`add-cube-cbrt`
18×	`times-frac` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
14×	`sqr-pow`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube`
3×	`distribute-lft-out`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 109

Calls

4 calls:

6.0ms	(pow x (/ 1.0 n))
18.0ms	(pow (+ x 1.0) (/ 1.0 n))
216.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
93.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

85.0ms	(pow x (/ 1.0 n))
253.0ms	(pow (+ x 1.0) (/ 1.0 n))
368.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
390.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.8s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	2306
1	629
0	234

prune814.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.5b

localize71.0ms

Local error

Found 4 expressions with local error:

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

rewrite428.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`unpow-prod-down`
36×	`difference-of-squares`
34×	`*-un-lft-identity`
24×	`sqr-pow`
16×	`log-pow`
15×	`exp-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `log-prod`
4×	`sub-neg` `add-cbrt-cube` `add-exp-log` `distribute-lft-out`
3×	`flip3--` `diff-log` `flip--`
2×	`exp-sum`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 102

Calls

4 calls:

197.0ms	(log (exp (- (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)))
65.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
71.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series2.1s

Counts

4 → 12

Calls

4 calls:

381.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
360.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
449.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
892.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.8s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
3	4846
2	915
1	306
0	141

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.5b

localize62.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.1b	(log (* (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))

rewrite543.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
30×	`unpow-prod-down`
27×	`difference-of-squares`
25×	`*-un-lft-identity`
18×	`sqr-pow`
12×	`pow1`
10×	`add-log-exp`
9×	`log-pow` `distribute-lft-out--`
7×	`add-exp-log`
6×	`pow1/3`
4×	`cbrt-div` `add-cbrt-cube` `exp-diff` `add-cube-cbrt`
3×	`log-div` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
2×	`rem-log-exp` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `log-prod` `pow-plus` `associate-l/` `prod-exp` `associate-r/`

Counts

4 → 94

Calls

4 calls:

107.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
73.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
122.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
237.0ms	(log (* (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))

series2.1s

Counts

4 → 12

Calls

4 calls:

463.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
414.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
391.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
791.0ms	(log (* (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))

simplify1.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1030
1	321
0	137

prune960.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 14.5b

regimes432.0ms

Accuracy

85.2% (1.3b remaining)

Error of 22.0b against oracle of 20.7b and baseline of 29.6b

bsearch262.0ms

Steps

Iters	Range		Point
10	5.808149794101367e-16	1126.7541422477805	1096.3579088579716
8	-118939140946.09552	-31677438.02179023	-47651231.91183168

simplify13.0ms

Iterations

Iter	Nodes
done	40
1	40
0	32

end0.0ms

sample8.2s

Algorithm

intervals

Results

2.8s	3133×	body	1280	valid
1.0s	1656×	body	640	valid
938.0ms	1146×	body	10240	exit
869.0ms	4662×	body	80	valid
585.0ms	629×	body	1280	nan
394.0ms	5035×	body	80	nan
389.0ms	631×	body	640	nan
307.0ms	884×	body	320	valid
169.0ms	397×	body	320	nan
97.0ms	453×	body	160	valid
33.0ms	171×	body	160	nan