Details

sample294.0ms

Algorithm

intervals

Results

86.0ms	92×	body	1280	valid
42.0ms	54×	body	640	valid
28.0ms	13×	body	320	nan
24.0ms	29×	body	10240	exit
21.0ms	15×	body	1280	nan
20.0ms	138×	body	80	valid
18.0ms	169×	body	80	nan
16.0ms	20×	body	640	nan
14.0ms	28×	body	320	valid
4.0ms	11×	body	160	valid
2.0ms	5×	body	160	nan

simplify25.0ms

Calls

1 calls:

Slowest

25.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize30.0ms

Local error

Found 3 expressions with local error:

1.8b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.8b	(pow x (/ 1 n))
0.5b	(pow (+ x 1) (/ 1 n))

rewrite21.0ms

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

18.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.0ms	(pow (+ x 1) (/ 1 n))
1.0ms	(pow x (/ 1 n))

series809.0ms

Calls

3 calls:

Slowest

649.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
91.0ms	(pow (+ x 1) (/ 1 n))
69.0ms	(pow x (/ 1 n))

simplify1.7s

Calls

28 calls:

Slowest

343.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
302.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
202.0ms	(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))
195.0ms	(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
194.0ms	(- (+ (/ (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))))

prune557.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.2b

localize9.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.8b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.8b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.8b	(pow x (/ 1 n))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

14.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
11.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
10.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.0ms	(pow x (/ 1 n))

series632.0ms

Calls

4 calls:

Slowest

202.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
183.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
170.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
77.0ms	(pow x (/ 1 n))

simplify2.3s

Calls

34 calls:

Slowest

312.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
288.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
272.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
257.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
209.0ms	(- (+ (/ (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

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* n x))
0.5b	(/ (log x) (* n (* n x)))
0.2b	(* n (* n x))
0.1b	(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))

rewrite38.0ms

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

17.0ms	(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))
16.0ms	(/ (log x) (* n (* n x)))
2.0ms	(* n (* n x))
2.0ms	(/ 1 (* n x))

series161.0ms

Calls

4 calls:

Slowest

99.0ms	(/ (log x) (* n (* n x)))
33.0ms	(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))
16.0ms	(* n (* n x))
13.0ms	(/ 1 (* n x))

simplify3.7s

Calls

42 calls:

Slowest

787.0ms	(* -1 (/ (log (/ 1 x)) (* x (pow n 2))))
244.0ms	(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))
234.0ms	(* (+ (pow (/ -1/2 x) 3) (pow 1 3)) 1)
199.0ms	(- (/ 1 (* x n)) (* 1/2 (/ 1 (* (pow x 2) n))))
194.0ms	(* -1 (/ (- (log (/ -1 x)) (log -1)) (* x (pow n 2))))

prune824.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.9b

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (log x) (* n (* n x)))
0.5b	(/ (/ 1 n) x)
0.2b	(* n (* n x))
0.1b	(* (+ (/ -1/2 x) 1) (/ (/ 1 n) x))

rewrite18.0ms

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

9.0ms	(* (+ (/ -1/2 x) 1) (/ (/ 1 n) x))
4.0ms	(/ (log x) (* n (* n x)))
3.0ms	(/ (/ 1 n) x)
1.0ms	(* n (* n x))

series136.0ms

Calls

4 calls:

Slowest

81.0ms	(/ (log x) (* n (* n x)))
31.0ms	(* (+ (/ -1/2 x) 1) (/ (/ 1 n) x))
15.0ms	(* n (* n x))
9.0ms	(/ (/ 1 n) x)

simplify4.2s

Calls

40 calls:

Slowest

729.0ms	(* -1 (/ (log (/ 1 x)) (* x (pow n 2))))
422.0ms	(* (- (* (/ -1/2 x) (/ -1/2 x)) (* 1 1)) (/ (/ 1 n) x))
377.0ms	(* (- (* (/ -1/2 x) (/ -1/2 x)) (* 1 1)) (/ 1 n))
278.0ms	(* (+ (pow (/ -1/2 x) 3) (pow 1 3)) (/ 1 n))
247.0ms	(* (+ (* (/ -1/2 x) (/ -1/2 x)) (- (* 1 1) (* (/ -1/2 x) 1))) x)

prune753.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.8b

regimes502.0ms

Accuracy

83.9% (1.4b remaining)

Error of 21.7b against oracle of 20.3b and baseline of 29.0b

bsearch9.0ms

end0.0ms

sample10.8s

Algorithm

intervals

Results

3.7s	3148×	body	1280	valid
1.8s	1102×	body	10240	exit
1.3s	1580×	body	640	valid
832.0ms	4647×	body	80	valid
772.0ms	613×	body	1280	nan
677.0ms	4985×	body	80	nan
522.0ms	652×	body	640	nan
492.0ms	884×	body	320	valid
169.0ms	349×	body	320	nan
155.0ms	411×	body	160	valid
56.0ms	188×	body	160	nan