Details

sample355.0ms

Algorithm

intervals

Results

109.0ms	107×	body	1280	valid
52.0ms	48×	body	10240	exit
45.0ms	157×	body	80	valid
40.0ms	49×	body	640	valid
32.0ms	29×	body	1280	nan
18.0ms	155×	body	80	nan
15.0ms	31×	body	320	valid
12.0ms	15×	body	640	nan
5.0ms	13×	body	320	nan
3.0ms	9×	body	160	valid
3.0ms	8×	body	160	nan

simplify28.0ms

Calls

1 calls:

Slowest

28.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize29.0ms

Local error

Found 3 expressions with local error:

1.2b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.5b	(pow (+ x 1) (/ 1 n))
0.2b	(pow x (/ 1 n))

rewrite42.0ms

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

37.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.0ms	(pow (+ x 1) (/ 1 n))
1.0ms	(pow x (/ 1 n))

series340.0ms

Calls

3 calls:

Slowest

171.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
84.0ms	(pow x (/ 1 n))
84.0ms	(pow (+ x 1) (/ 1 n))

simplify3.7s

Calls

69 calls:

Slowest

340.0ms	(- (/ 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))
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))))
193.0ms	(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
180.0ms	(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))

prune838.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.6b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
1.1b	(log (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))
0.5b	(pow (+ 1 x) (/ 1 n))
0.2b	(pow x (/ 1 n))

rewrite43.0ms

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

25.0ms	(log (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))
13.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
2.0ms	(pow (+ 1 x) (/ 1 n))
1.0ms	(pow x (/ 1 n))

series577.0ms

Calls

4 calls:

Slowest

222.0ms	(log (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))
201.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
88.0ms	(pow (+ 1 x) (/ 1 n))
65.0ms	(pow x (/ 1 n))

simplify6.8s

Calls

103 calls:

Slowest

413.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
369.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
282.0ms	(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
266.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
259.0ms	(- (+ (/ (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))))

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.6b

localize23.0ms

Local error

Found 4 expressions with local error:

1.3b	(log (* (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))))
1.2b	(log (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
1.2b	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
1.2b	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt` `prod-diff`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
35×	`unpow-prod-down`
27×	`log-prod`
23×	`cbrt-prod`
20×	`exp-sum`
12×	`fma-neg`
11×	`pow1`
9×	`log-pow`
8×	`add-exp-log` `add-log-exp`
5×	`cbrt-div` `exp-diff` `pow1/3`
4×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `rem-log-exp`
2×	`flip3--` `diff-log` `pow-prod-down` `pow-prod-up` `flip--` `distribute-lft-out--`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/`

Calls

4 calls:

Slowest

46.0ms	(log (* (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))))
24.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
23.0ms	(log (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
23.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))

series1.0s

Calls

4 calls:

Slowest

348.0ms	(log (* (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))))
307.0ms	(log (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
211.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
179.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))

simplify8.9s

Calls

143 calls:

Slowest

424.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
340.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
276.0ms	(log (pow (pow (exp (- 1 (exp (/ (log x) n)))) 2) 1/3))
270.0ms	(- (* 1/3 (/ 1 (* x n))) (+ (* 1/3 (/ (log (/ 1 x)) (* x (pow n 2)))) (* 1/6 (/ 1 (* (pow x 2) n)))))
240.0ms	(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))

prune2.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.1b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b	(log (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
1.2b	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
1.2b	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
1.2b	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt` `prod-diff`
66×	`*-un-lft-identity`
60×	`add-cube-cbrt`
48×	`unpow-prod-down`
26×	`log-prod`
23×	`cbrt-prod`
20×	`exp-sum`
18×	`fma-neg`
10×	`add-log-exp`
6×	`difference-of-squares`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--` `distribute-lft-out--`
2×	`log-pow`
1×	`log-div` `cbrt-div` `exp-diff` `pow1/3` `rem-log-exp`

Calls

4 calls:

Slowest

21.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
21.0ms	(log (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
14.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
13.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))

series905.0ms

Calls

4 calls:

Slowest

295.0ms	(log (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
231.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
196.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
182.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))

simplify11.2s

Calls

181 calls:

Slowest

471.0ms	(fma (* (cbrt (pow (+ 1 x) (/ 1 n))) (cbrt (pow (+ 1 x) (/ 1 n)))) (cbrt (pow (+ 1 x) (/ 1 n))) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))
348.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
324.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
307.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
269.0ms	(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))

prune3.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.1b

regimes303.0ms

Accuracy

71.4% (4.0b remaining)

Error of 19.6b against oracle of 15.6b and baseline of 29.6b

bsearch1.2s

end0.0ms

sample10.7s

Algorithm

intervals

Results

3.4s	3151×	body	1280	valid
1.7s	1236×	body	10240	exit
1.2s	1569×	body	640	valid
1.0s	4998×	body	80	nan
827.0ms	4765×	body	80	valid
764.0ms	669×	body	1280	nan
518.0ms	852×	body	320	valid
469.0ms	630×	body	640	nan
176.0ms	356×	body	320	nan
152.0ms	455×	body	160	valid
54.0ms	204×	body	160	nan