Details

sample275.0ms

Algorithm

intervals

Results

80.0ms	91×	body	1280	valid
37.0ms	40×	body	10240	exit
34.0ms	55×	body	640	valid
31.0ms	30×	body	1280	nan
22.0ms	170×	body	80	valid
18.0ms	181×	body	80	nan
14.0ms	21×	body	640	nan
13.0ms	29×	body	320	valid
6.0ms	14×	body	320	nan
3.0ms	13×	body	160	valid
0.0ms	1×	body	160	nan

simplify55.0ms

Calls

1 calls:

Slowest

55.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize30.0ms

Local error

Found 3 expressions with local error:

2.3b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.2b	(pow (+ x 1) (/ 1 n))
1.0b	(pow x (/ 1 n))

rewrite25.0ms

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

20.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.0ms	(pow (+ x 1) (/ 1 n))
1.0ms	(pow x (/ 1 n))

series384.0ms

Calls

3 calls:

Slowest

228.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
79.0ms	(pow (+ x 1) (/ 1 n))
78.0ms	(pow x (/ 1 n))

simplify1.7s

Calls

28 calls:

Slowest

350.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
312.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
224.0ms	(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))
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)))))
192.0ms	(- (+ (/ (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))))

prune540.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.3b

localize8.0ms

Local error

Found 4 expressions with local error:

3.5b	(- (pow (+ x 1) (/ 1 n)) (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n)))))
2.2b	(pow (+ x 1) (/ 1 n))
1.0b	(pow x (/ 1 n))
1.0b	(pow x (/ 1 n))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

9.0ms	(- (pow (+ x 1) (/ 1 n)) (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n)))))
4.0ms	(pow x (/ 1 n))
2.0ms	(pow (+ x 1) (/ 1 n))
1.0ms	(pow x (/ 1 n))

series421.0ms

Calls

4 calls:

Slowest

198.0ms	(- (pow (+ x 1) (/ 1 n)) (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n)))))
77.0ms	(pow x (/ 1 n))
77.0ms	(pow (+ x 1) (/ 1 n))
70.0ms	(pow x (/ 1 n))

simplify2.2s

Calls

34 calls:

Slowest

302.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
300.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
277.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
242.0ms	(- (+ (/ (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))))
210.0ms	(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))

prune809.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 22.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (log x) (* n (* n x)))
0.6b	(/ 1 (* n x))
0.1b	(* n (* n x))
0.1b	(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
7×	`pow1`
5×	`associate-r`
4×	`insert-posit16` `add-log-exp`
3×	`times-frac` `associate-l` `div-inv` `associate-/l*`
2×	`frac-times` `rec-exp` `clear-num` `associate-/r` `frac-2neg` `flip3-+` `associate-l/` `prod-exp` `*-commutative` `flip-+`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-*r/` `un-div-inv` `cbrt-unprod` `pow-flip` `inv-pow`

Calls

4 calls:

Slowest

14.0ms	(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))
5.0ms	(/ (log x) (* n (* n x)))
2.0ms	(* n (* n x))
1.0ms	(/ 1 (* n x))

series137.0ms

Calls

4 calls:

Slowest

77.0ms	(/ (log x) (* n (* n x)))
31.0ms	(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))
18.0ms	(* n (* n x))
11.0ms	(/ 1 (* n x))

simplify4.0s

Calls

42 calls:

Slowest

795.0ms	(* -1 (/ (log (/ 1 x)) (* x (pow n 2))))
295.0ms	(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))
233.0ms	(* (+ (pow (/ -1/2 x) 3) (pow 1 3)) 1)
233.0ms	(- (/ 1 (* x n)) (* 1/2 (/ 1 (* (pow x 2) n))))
218.0ms	(/ (* (* (log x) (log x)) (log x)) (* (* (* n (* n x)) (* n (* n x))) (* n (* n x))))

prune914.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (log x) (* n (* n x)))
0.2b	(/ (/ 1 n) x)
0.1b	(* n (* n x))
0.1b	(* (+ (/ -1/2 x) 1) (/ (/ 1 n) x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/l*`
6×	`pow1`
5×	`associate-r`
4×	`insert-posit16` `div-inv` `add-log-exp`
3×	`times-frac` `associate-l`
2×	`frac-times` `clear-num` `frac-2neg` `flip3-+` `associate-l/` `-commutative` `flip-+`
1×	`cbrt-undiv` `associate-/r` `div-exp` `pow-prod-down` `prod-exp` `associate-r/` `cbrt-unprod` `associate-/l/`

Calls

4 calls:

Slowest

13.0ms	(* (+ (/ -1/2 x) 1) (/ (/ 1 n) x))
5.0ms	(/ (log x) (* n (* n x)))
3.0ms	(/ (/ 1 n) x)
1.0ms	(* n (* n x))

series145.0ms

Calls

4 calls:

Slowest

86.0ms	(/ (log x) (* n (* n x)))
32.0ms	(* (+ (/ -1/2 x) 1) (/ (/ 1 n) x))
17.0ms	(* n (* n x))
10.0ms	(/ (/ 1 n) x)

simplify4.4s

Calls

40 calls:

Slowest

706.0ms	(* -1 (/ (log (/ 1 x)) (* x (pow n 2))))
520.0ms	(* (- (* (/ -1/2 x) (/ -1/2 x)) (* 1 1)) (/ (/ 1 n) x))
415.0ms	(* (- (* (/ -1/2 x) (/ -1/2 x)) (* 1 1)) (/ 1 n))
264.0ms	(* (+ (* (/ -1/2 x) (/ -1/2 x)) (- (* 1 1) (* (/ -1/2 x) 1))) x)
224.0ms	(* (+ (pow (/ -1/2 x) 3) (pow 1 3)) (/ 1 n))

prune793.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.7b

regimes345.0ms

Accuracy

83.3% (1.5b remaining)

Error of 22.1b against oracle of 20.7b and baseline of 29.4b

bsearch261.0ms

end0.0ms

sample10.7s

Algorithm

intervals

Results

4.0s	3180×	body	1280	valid
1.3s	1185×	body	10240	exit
1.3s	1584×	body	640	valid
791.0ms	4742×	body	80	valid
775.0ms	637×	body	1280	nan
712.0ms	5179×	body	80	nan
595.0ms	672×	body	640	nan
480.0ms	857×	body	320	valid
149.0ms	322×	body	320	nan
144.0ms	442×	body	160	valid
53.0ms	191×	body	160	nan