Details

sample391.0ms

Algorithm

intervals

Results

125.0ms	107×	body	1280	valid
57.0ms	48×	body	10240	exit
42.0ms	49×	body	640	valid
34.0ms	29×	body	1280	nan
31.0ms	8×	body	160	nan
25.0ms	157×	body	80	valid
19.0ms	155×	body	80	nan
15.0ms	31×	body	320	valid
11.0ms	15×	body	640	nan
7.0ms	13×	body	320	nan
3.0ms	9×	body	160	valid

simplify23.0ms

Calls

1 calls:

Slowest

23.0ms

(- (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

localize33.0ms

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))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`pow-unpow` `*-un-lft-identity`
6×	`add-cube-cbrt`
5×	`add-log-exp`
4×	`pow1` `unpow-prod-down` `add-exp-log`
3×	`add-cbrt-cube` `insert-posit16`
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

14.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.0ms	(pow (+ x 1) (/ 1 n))
1.0ms	(pow x (/ 1 n))

series376.0ms

Calls

3 calls:

Slowest

198.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
90.0ms	(pow (+ x 1) (/ 1 n))
88.0ms	(pow x (/ 1 n))

simplify1.7s

Calls

28 calls:

Slowest

333.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
304.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
226.0ms	(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
206.0ms	(- (+ (/ (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))))
191.0ms	(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))

prune557.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.8b

localize17.0ms

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))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cube-cbrt`
8×	`pow-unpow`
7×	`log-pow`
6×	`pow1` `exp-prod` `add-log-exp`
5×	`log-prod` `unpow-prod-down` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `difference-of-squares`
2×	`pow-to-exp` `sub-neg` `exp-sum` `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

23.0ms	(log (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))
10.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
2.0ms	(pow (+ 1 x) (/ 1 n))
1.0ms	(pow x (/ 1 n))

series563.0ms

Calls

4 calls:

Slowest

224.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
180.0ms	(log (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))
85.0ms	(pow x (/ 1 n))
75.0ms	(pow (+ 1 x) (/ 1 n))

simplify2.5s

Calls

44 calls:

Slowest

310.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
305.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
305.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
211.0ms	(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))
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)))))

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.8b

localize29.0ms

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)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`pow1`
10×	`*-un-lft-identity`
9×	`log-prod` `log-pow`
8×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt`
5×	`cbrt-prod` `cbrt-div` `exp-diff` `pow1/3`
4×	`log-div` `add-cbrt-cube` `insert-posit16` `difference-of-squares`
3×	`sub-neg` `rem-log-exp`
2×	`unpow-prod-down` `flip3--` `diff-log` `exp-sum` `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

36.0ms	(log (* (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))))
18.0ms	(log (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
12.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
11.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))

series1.0s

Calls

4 calls:

Slowest

373.0ms	(log (* (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))))
288.0ms	(log (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
206.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
182.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))

simplify3.8s

Calls

43 calls:

Slowest

387.0ms	(- (+ (* 2/3 (/ (log -1) (* x (pow n 2)))) (* 2/3 (/ 1 (* x n)))) (+ (* 1/3 (/ 1 (* (pow x 2) n))) (* 2/3 (/ (log (/ -1 x)) (* x (pow n 2))))))
358.0ms	(- (+ (* 1/3 (/ (log -1) (* x (pow n 2)))) (* 1/3 (/ 1 (* x n)))) (+ (* 1/6 (/ 1 (* (pow x 2) n))) (* 1/3 (/ (log (/ -1 x)) (* x (pow n 2))))))
348.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
300.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
256.0ms	(- (* 2/3 (/ 1 (* x n))) (+ (* 2/3 (/ (log (/ 1 x)) (* x (pow n 2)))) (* 1/3 (/ 1 (* (pow x 2) n)))))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.7b

localize21.0ms

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)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`log-prod`
6×	`add-cube-cbrt` `difference-of-squares`
5×	`cbrt-prod` `pow1` `add-exp-log`
4×	`sub-neg` `add-cbrt-cube` `insert-posit16`
3×	`unpow-prod-down` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
2×	`exp-sum` `log-pow`
1×	`log-div` `cbrt-div` `exp-diff` `pow1/3` `rem-log-exp`

Calls

4 calls:

Slowest

14.0ms	(log (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
12.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
11.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
11.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))

series897.0ms

Calls

4 calls:

Slowest

311.0ms	(log (cbrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
215.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
191.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
180.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))

simplify3.3s

Calls

40 calls:

Slowest

356.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
350.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
349.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
342.0ms	(- (+ (* 1/3 (/ (log -1) (* x (pow n 2)))) (* 1/3 (/ 1 (* x n)))) (+ (* 1/6 (/ 1 (* (pow x 2) n))) (* 1/3 (/ (log (/ -1 x)) (* x (pow n 2))))))
256.0ms	(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 20.7b

regimes375.0ms

Accuracy

81.2% (1.6b remaining)

Error of 22.6b against oracle of 21.0b and baseline of 29.6b

bsearch10.0ms

end0.0ms

sample10.5s

Algorithm

intervals

Results

3.7s	3151×	body	1280	valid
1.6s	1569×	body	640	valid
1.3s	1236×	body	10240	exit
770.0ms	669×	body	1280	nan
767.0ms	4765×	body	80	valid
679.0ms	4998×	body	80	nan
454.0ms	630×	body	640	nan
409.0ms	852×	body	320	valid
169.0ms	455×	body	160	valid
165.0ms	356×	body	320	nan
55.0ms	204×	body	160	nan