Details

sample254.0ms

Algorithm

intervals

Results

75.0ms	99×	body	1280	valid
29.0ms	52×	body	640	valid
28.0ms	30×	body	640	nan
19.0ms	23×	body	1280	nan
14.0ms	28×	body	10240	exit
14.0ms	144×	body	80	valid
13.0ms	173×	body	80	nan
12.0ms	34×	body	320	valid
4.0ms	10×	body	320	nan
3.0ms	12×	body	160	valid
1.0ms	4×	body	160	nan

simplify979.0ms

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize29.0ms

Local error

Found 3 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite123.0ms

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))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
107.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series577.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(pow x (/ 1.0 n))
188.0ms	(pow (+ x 1.0) (/ 1.0 n))
300.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	2073
1	544
0	189

prune520.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.2b	(pow (+ 1.0 x) (/ 1.0 n))
2.2b	(log (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))))
2.2b	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite374.0ms

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:

3.0ms	(pow x (/ 1.0 n))
14.0ms	(pow (+ 1.0 x) (/ 1.0 n))
238.0ms	(log (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))))
115.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.0s

Counts

4 → 12

Calls

4 calls:

74.0ms	(pow x (/ 1.0 n))
177.0ms	(pow (+ 1.0 x) (/ 1.0 n))
374.0ms	(log (exp (- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))))
400.0ms	(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.2s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	2304
1	629
0	234

prune813.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 20.2b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
30×	`unpow-prod-down`
27×	`difference-of-squares`
26×	`*-un-lft-identity`
18×	`sqr-pow`
11×	`add-log-exp`
9×	`distribute-lft-out--`
5×	`pow1` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log`
3×	`log-prod` `sub-neg` `flip3--` `diff-log` `log-pow` `flip--` `distribute-lft-out`
1×	`exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 86

Calls

4 calls:

6.0ms	(log (exp (* (* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))
82.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
75.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
111.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.7s

Counts

4 → 12

Calls

4 calls:

447.0ms	(log (exp (* (* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))
365.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
413.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
445.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.0s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
3	4030
2	754
1	248
0	114

prune754.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.2b

localize113.0ms

Local error

Found 4 expressions with local error:

2.2b	(log (exp (* (* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))))))))
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)))
3.4b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
30×	`difference-of-squares`
27×	`unpow-prod-down`
21×	`*-un-lft-identity`
19×	`sqr-pow`
11×	`add-log-exp`
9×	`sqrt-prod`
7×	`distribute-lft-out--`
5×	`pow1` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log`
3×	`log-prod` `sub-neg` `flip3--` `diff-log` `log-pow` `flip--`
2×	`distribute-lft-out`
1×	`exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 87

Calls

4 calls:

3.0ms	(log (exp (* (* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))))))))
79.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
83.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
96.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

series39.0s

Counts

4 → 12

Calls

4 calls:

37.7s	(log (exp (* (* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))))))))
366.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
366.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
522.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

simplify485.0ms

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
1	1057
0	359

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 20.1b

regimes357.0ms

Accuracy

80.9% (1.7b remaining)

Error of 22.0b against oracle of 20.3b and baseline of 29.1b

bsearch1.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	58
2	58
1	56
0	44

end0.0ms

sample8.0s

Algorithm

intervals

Results

2.4s	3156×	body	1280	valid
1.1s	1213×	body	10240	exit
950.0ms	1585×	body	640	valid
808.0ms	4883×	body	80	valid
489.0ms	641×	body	1280	nan
425.0ms	5247×	body	80	nan
373.0ms	677×	body	640	nan
311.0ms	837×	body	320	valid
111.0ms	378×	body	320	nan
110.0ms	204×	body	160	nan
97.0ms	467×	body	160	valid