Details

sample346.0ms

Algorithm

intervals

Results

104.0ms	99×	body	1280	valid
48.0ms	53×	body	640	valid
36.0ms	11×	body	160	valid
32.0ms	31×	body	10240	exit
31.0ms	27×	body	1280	nan
21.0ms	144×	body	80	valid
16.0ms	140×	body	80	nan
14.0ms	25×	body	320	valid
12.0ms	17×	body	640	nan
7.0ms	14×	body	320	nan
2.0ms	6×	body	160	nan

simplify14.0ms

Calls

1 calls:

Slowest

14.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize17.0ms

Local error

Found 3 expressions with local error:

1.5b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.5b	(pow x (/ 1 n))
0.5b	(pow (+ x 1) (/ 1 n))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`unpow-prod-down`
8×	`pow-unpow`
6×	`fma-neg`
5×	`add-log-exp`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`pow-to-exp` `div-inv` `difference-of-squares`
1×	`sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `flip--` `distribute-lft-out--`

Calls

3 calls:

Slowest

25.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
4.0ms	(pow (+ x 1) (/ 1 n))
2.0ms	(pow x (/ 1 n))

series484.0ms

Calls

3 calls:

Slowest

297.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
111.0ms	(pow (+ x 1) (/ 1 n))
76.0ms	(pow x (/ 1 n))

simplify3.7s

Calls

69 calls:

Slowest

391.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
355.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
276.0ms	(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))
222.0ms	(- (+ (/ (log -1) n) (+ (* 1/2 (/ (pow (log -1) 2) (pow n 2))) (+ (* 1/2 (/ (pow (log (/ -1 x)) 2) (pow n 2))) 1))) (+ (/ (log (/ -1 x)) n) (/ (* (log (/ -1 x)) (log -1)) (pow n 2))))
204.0ms	(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))

prune958.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.8b

localize5.0ms

Local error

Found 4 expressions with local error:

1.5b	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
1.5b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.5b	(pow x (/ 1 n))
0.5b	(pow (+ x 1) (/ 1 n))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
36×	`prod-diff`
35×	`add-cube-cbrt`
26×	`unpow-prod-down`
23×	`log-prod`
20×	`exp-sum`
8×	`pow-unpow`
7×	`log-pow`
6×	`pow1` `exp-prod` `fma-neg` `add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`pow-to-exp` `sub-neg` `div-inv` `distribute-lft-out--`
1×	`log-div` `pow-pow` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-exp` `flip--`

Calls

4 calls:

Slowest

24.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
23.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
4.0ms	(pow (+ x 1) (/ 1 n))
2.0ms	(pow x (/ 1 n))

series605.0ms

Calls

4 calls:

Slowest

231.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
201.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
110.0ms	(pow (+ x 1) (/ 1 n))
62.0ms	(pow x (/ 1 n))

simplify6.4s

Calls

103 calls:

Slowest

329.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
321.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
296.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
257.0ms	(- (+ (/ (log -1) n) (+ (* 1/2 (/ (pow (log -1) 2) (pow n 2))) (+ (* 1/2 (/ (pow (log (/ -1 x)) 2) (pow n 2))) 1))) (+ (/ (log (/ -1 x)) n) (/ (* (log (/ -1 x)) (log -1)) (pow n 2))))
215.0ms	(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.8b

localize19.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.5b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.5b	(pow x (/ 1 n))
0.5b	(pow x (/ 1 n))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
26×	`unpow-prod-down`
12×	`fma-neg`
8×	`pow-unpow` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `div-inv` `flip--` `distribute-lft-out--`

Calls

4 calls:

Slowest

15.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
15.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.0ms	(pow x (/ 1 n))
1.0ms	(pow x (/ 1 n))

series663.0ms

Calls

4 calls:

Slowest

269.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
241.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
77.0ms	(pow x (/ 1 n))
75.0ms	(pow x (/ 1 n))

simplify6.5s

Calls

114 calls:

Slowest

390.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
389.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
308.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
288.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
284.0ms	(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.8b

localize20.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (pow (+ x 1) (/ 1 n)) (log (exp (pow x (/ 1 n)))))
1.5b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.6b	(log (exp (sqrt (- (pow (+ x 1) (/ 1 n)) (log (exp (pow x (/ 1 n))))))))
0.5b	(pow x (/ 1 n))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
60×	`prod-diff`
59×	`*-un-lft-identity`
51×	`add-cube-cbrt`
39×	`unpow-prod-down`
37×	`log-pow`
28×	`exp-prod`
13×	`pow1`
12×	`fma-neg`
7×	`sqrt-prod` `add-log-exp`
6×	`log-prod` `difference-of-squares`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow-unpow` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`associate--r+`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `rem-log-exp` `div-inv`

Calls

4 calls:

Slowest

61.0ms	(log (exp (sqrt (- (pow (+ x 1) (/ 1 n)) (log (exp (pow x (/ 1 n))))))))
32.0ms	(- (pow (+ x 1) (/ 1 n)) (log (exp (pow x (/ 1 n)))))
24.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.0ms	(pow x (/ 1 n))

series1.1s

Calls

4 calls:

Slowest

418.0ms	(log (exp (sqrt (- (pow (+ x 1) (/ 1 n)) (log (exp (pow x (/ 1 n))))))))
290.0ms	(- (pow (+ x 1) (/ 1 n)) (log (exp (pow x (/ 1 n)))))
263.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
83.0ms	(pow x (/ 1 n))

simplify9.9s

Calls

176 calls:

Slowest

373.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
363.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
355.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
261.0ms	(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
244.0ms	(- (+ (/ (log -1) n) (+ (* 1/2 (/ (pow (log -1) 2) (pow n 2))) (+ (* 1/2 (/ (pow (log (/ -1 x)) 2) (pow n 2))) 1))) (+ (/ (log (/ -1 x)) n) (/ (* (log (/ -1 x)) (log -1)) (pow n 2))))

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.8b

regimes371.0ms

Accuracy

88.7% (1.3b remaining)

Error of 19.2b against oracle of 17.9b and baseline of 29.2b

bsearch8.0ms

end0.0ms

sample10.3s

Algorithm

intervals

Results

3.6s	3158×	body	1280	valid
1.7s	1631×	body	640	valid
1.2s	1099×	body	10240	exit
727.0ms	672×	body	1280	nan
713.0ms	5011×	body	80	nan
689.0ms	4671×	body	80	valid
483.0ms	608×	body	640	nan
430.0ms	844×	body	320	valid
178.0ms	425×	body	160	valid
157.0ms	333×	body	320	nan
48.0ms	170×	body	160	nan