Details

sample338.0ms

Algorithm

intervals

Results

101.0ms	104×	body	1280	valid
50.0ms	41×	body	10240	exit
46.0ms	152×	body	80	valid
35.0ms	51×	body	640	valid
20.0ms	22×	body	1280	nan
18.0ms	36×	body	320	valid
17.0ms	167×	body	80	nan
13.0ms	20×	body	640	nan
6.0ms	14×	body	320	nan
5.0ms	15×	body	160	valid
1.0ms	3×	body	160	nan

simplify255.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

254.0ms

(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize30.0ms

Local error

Found 3 expressions with local error:

3.3b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.7b	(pow (+ x 1) (/ 1 n))
0.3b	(pow x (/ 1 n))

rewrite97.0ms

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` `insert-posit16` `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 → 82

Calls

3 calls:

Slowest

85.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
7.0ms	(pow (+ x 1) (/ 1 n))
3.0ms	(pow x (/ 1 n))

series464.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

250.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
117.0ms	(pow (+ x 1) (/ 1 n))
98.0ms	(pow x (/ 1 n))

simplify10.0s

Counts

69 → 91

Calls

69 calls:

Slowest

635.0ms	(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
536.0ms	(+ (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))
524.0ms	(+ (sqrt (pow (+ x 1) (/ 1 n))) (pow (sqrt x) (/ 1 n)))
522.0ms	(- (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))
483.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))

prune976.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.9b

localize57.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
0.7b	(pow (+ x 1) (/ 1 n))
0.3b	(pow x (/ 1 n))
0.3b	(pow x (/ 1 n))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
30×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
10×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube` `insert-posit16`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `sqr-pow`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`

Counts

4 → 98

Calls

4 calls:

Slowest

61.0ms	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
7.0ms	(pow (+ x 1) (/ 1 n))
5.0ms	(pow x (/ 1 n))
5.0ms	(pow x (/ 1 n))

series462.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

248.0ms	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
93.0ms	(pow (+ x 1) (/ 1 n))
66.0ms	(pow x (/ 1 n))
56.0ms	(pow x (/ 1 n))

simplify4.0s

Counts

66 → 110

Calls

66 calls:

Slowest

558.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
483.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
409.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
386.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
333.0ms	(/ (exp (pow (+ x 1) (/ 1 n))) (exp (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n))))))

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.9b

localize72.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
3.8b	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
3.8b	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
0.7b	(pow (+ x 1) (/ 1 n))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
13×	`pow-unpow`
12×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac`
5×	`pow1` `add-exp-log`
4×	`unpow-prod-down` `add-cbrt-cube` `insert-posit16`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

Slowest

93.0ms	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
89.0ms	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
68.0ms	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
14.0ms	(pow (+ x 1) (/ 1 n))

series918.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

297.0ms	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
263.0ms	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
222.0ms	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
135.0ms	(pow (+ x 1) (/ 1 n))

simplify4.4s

Counts

34 → 80

Calls

34 calls:

Slowest

768.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
422.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
386.0ms	(/ (exp (pow (+ x 1) (/ 1 n))) (exp (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n))))))
375.0ms	(/ (exp (pow (+ x 1) (/ 1 n))) (exp (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n))))))
367.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.9b

localize130.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
3.8b	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
3.8b	(- (pow (pow (+ x 1) (/ 1 (* (cbrt n) (cbrt n)))) (/ 1 (cbrt n))) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
0.9b	(pow (+ x 1) (/ 1 (* (cbrt n) (cbrt n))))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
9×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `pow-unpow` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`unpow-prod-down` `add-cbrt-cube` `insert-posit16`
3×	`sub-neg` `times-frac` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 62

Calls

4 calls:

Slowest

158.0ms	(- (pow (pow (+ x 1) (/ 1 (* (cbrt n) (cbrt n)))) (/ 1 (cbrt n))) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
92.0ms	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
62.0ms	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
8.0ms	(pow (+ x 1) (/ 1 (* (cbrt n) (cbrt n))))

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

486.0ms	(- (pow (pow (+ x 1) (/ 1 (* (cbrt n) (cbrt n)))) (/ 1 (cbrt n))) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
299.0ms	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
278.0ms	(- (pow (+ x 1) (/ 1 n)) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
215.0ms	(pow (+ x 1) (/ 1 (* (cbrt n) (cbrt n))))

simplify4.6s

Counts

28 → 74

Calls

28 calls:

Slowest

628.0ms	(- (+ (* 1/2 (* (/ (exp (* (/ (- (log -1) (log (/ -1 x))) (pow (cbrt -1) 2)) (pow (/ 1 (pow n 2)) 1/3))) (* (pow x 2) (pow (cbrt -1) 4))) (pow (/ 1 (pow n 4)) 1/3))) (+ (* (/ (exp (* (/ (- (log -1) (log (/ -1 x))) (pow (cbrt -1) 2)) (pow (/ 1 (pow n 2)) 1/3))) (* x (pow (cbrt -1) 2))) (pow (/ 1 (pow n 2)) 1/3)) (exp (* (/ (- (log -1) (log (/ -1 x))) (pow (cbrt -1) 2)) (pow (/ 1 (pow n 2)) 1/3))))) (* 1/2 (* (/ (exp (* (/ (- (log -1) (log (/ -1 x))) (pow (cbrt -1) 2)) (pow (/ 1 (pow n 2)) 1/3))) (* (pow x 2) (pow (cbrt -1) 2))) (pow (/ 1 (pow n 2)) 1/3))))
573.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 (* (cbrt n) (cbrt n))))
385.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
341.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
333.0ms	(/ (exp (pow (+ x 1) (/ 1 n))) (exp (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n))))))

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.9b

regimes330.0ms

Accuracy

81.4% (1.6b remaining)

Error of 23.1b against oracle of 21.5b and baseline of 30.2b

bsearch7.0ms

end0.0ms

sample11.6s

Algorithm

intervals

Results

4.1s	3240×	body	1280	valid
2.0s	1193×	body	10240	exit
1.4s	1606×	body	640	valid
921.0ms	4723×	body	80	valid
709.0ms	647×	body	1280	nan
623.0ms	5310×	body	80	nan
530.0ms	663×	body	640	nan
445.0ms	856×	body	320	valid
182.0ms	352×	body	320	nan
138.0ms	431×	body	160	valid
57.0ms	195×	body	160	nan