Details

sample343.0ms

Algorithm

intervals

Results

96.0ms	99×	body	1280	valid
49.0ms	46×	body	10240	exit
47.0ms	186×	body	80	valid
38.0ms	51×	body	640	valid
28.0ms	22×	body	1280	nan
21.0ms	194×	body	80	nan
16.0ms	29×	body	320	valid
13.0ms	20×	body	640	nan
6.0ms	13×	body	320	nan
4.0ms	13×	body	160	valid
2.0ms	6×	body	160	nan

simplify313.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

313.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize16.0ms

Local error

Found 3 expressions with local error:

1.5b	(pow (+ x 1) (/ 1 n))
1.3b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.3b	(pow x (/ 1 n))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 152

Calls

3 calls:

Slowest

88.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
8.0ms	(pow (+ x 1) (/ 1 n))
3.0ms	(pow x (/ 1 n))

series453.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

273.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
118.0ms	(pow (+ x 1) (/ 1 n))
61.0ms	(pow x (/ 1 n))

simplify40.1s

Counts

188 → 161

Calls

188 calls:

Slowest

721.0ms	(fma (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt (+ x 1)) (/ 1 n)) (- (* (pow x (/ 1 n)) 1)))
697.0ms	(* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n))))
571.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
555.0ms	(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
513.0ms	(- (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.9b

localize46.0ms

Local error

Found 4 expressions with local error:

2.2b	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (pow x (/ 1 n))))
1.5b	(pow (+ x 1) (/ 1 n))
1.5b	(pow (+ x 1) (/ 1 n))
0.3b	(pow x (/ 1 n))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
32×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
11×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `sqr-pow`
2×	`distribute-lft-out`
1×	`fma-udef`

Counts

4 → 103

Calls

4 calls:

Slowest

13.0ms	(pow (+ x 1) (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
3.0ms	(pow x (/ 1 n))
1.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (pow x (/ 1 n))))

series695.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

401.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (pow x (/ 1 n))))
115.0ms	(pow (+ x 1) (/ 1 n))
107.0ms	(pow (+ x 1) (/ 1 n))
72.0ms	(pow x (/ 1 n))

simplify3.3s

Counts

67 → 115

Calls

67 calls:

Slowest

403.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
370.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
340.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
326.0ms	(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
250.0ms	(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.9b

localize71.0ms

Local error

Found 4 expressions with local error:

2.2b	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (pow x (/ 1 n))))
2.2b	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (pow x (/ 1 n))))
2.2b	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (pow x (/ 1 n))))
1.5b	(pow (+ x 1) (/ 1 n))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
13×	`pow-unpow`
12×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`times-frac`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `unpow-prod-down` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

Slowest

15.0ms	(pow (+ x 1) (/ 1 n))
1.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (pow x (/ 1 n))))
0.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (pow x (/ 1 n))))
0.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (pow x (/ 1 n))))

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

421.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (pow x (/ 1 n))))
384.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (pow x (/ 1 n))))
380.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (pow x (/ 1 n))))
102.0ms	(pow (+ x 1) (/ 1 n))

simplify3.1s

Counts

31 → 76

Calls

31 calls:

Slowest

412.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
409.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
403.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
374.0ms	(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
295.0ms	(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.9b

localize35.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (exp (/ (log1p x) n)) (pow x (/ 1 n)))
0.3b	(pow x (/ 1 n))
0.1b	(/ (log1p x) n)
0.0b	(exp (/ (log1p x) n))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
41×	`add-cube-cbrt`
27×	`times-frac`
21×	`prod-diff`
13×	`pow-unpow` `exp-prod` `unpow-prod-down`
7×	`add-exp-log` `add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `sqr-pow`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `fma-neg` `div-inv` `associate-/l` `difference-of-squares`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `flip3--` `diff-log` `div-exp` `pow-exp` `flip--` `distribute-lft-out--` `rem-exp-log`

Counts

4 → 127

Calls

4 calls:

Slowest

29.0ms	(- (exp (/ (log1p x) n)) (pow x (/ 1 n)))
4.0ms	(/ (log1p x) n)
4.0ms	(exp (/ (log1p x) n))
3.0ms	(pow x (/ 1 n))

series544.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

259.0ms	(- (exp (/ (log1p x) n)) (pow x (/ 1 n)))
118.0ms	(exp (/ (log1p x) n))
85.0ms	(pow x (/ 1 n))
82.0ms	(/ (log1p x) n)

simplify19.2s

Counts

119 → 139

Calls

119 calls:

Slowest

656.0ms	(fma 1 (exp (/ (log1p x) n)) (- (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n))))))
650.0ms	(fma (sqrt (exp (/ (log1p x) n))) (sqrt (exp (/ (log1p x) n))) (- (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n))))))
618.0ms	(fma 1 (exp (/ (log1p x) n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))
618.0ms	(- (sqrt (exp (/ (log1p x) n))) (pow (sqrt x) (/ 1 n)))
569.0ms	(- (exp (/ (log1p x) n)) (pow x (/ 1 n)))

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.8b

regimes234.0ms

Accuracy

67.9% (3.6b remaining)

Error of 22.1b against oracle of 18.5b and baseline of 29.7b

bsearch9.0ms

end0.0ms

sample10.8s

Algorithm

intervals

Results

3.9s	3146×	body	1280	valid
1.5s	1130×	body	10240	exit
1.4s	1590×	body	640	valid
833.0ms	4735×	body	80	valid
821.0ms	706×	body	1280	nan
680.0ms	5086×	body	80	nan
462.0ms	610×	body	640	nan
449.0ms	880×	body	320	valid
262.0ms	345×	body	320	nan
142.0ms	437×	body	160	valid
56.0ms	189×	body	160	nan