Details

sample288.0ms

Algorithm

intervals

Results

100.0ms	104×	body	1280	valid
35.0ms	28×	body	10240	exit
27.0ms	39×	body	640	valid
27.0ms	24×	body	1280	nan
20.0ms	37×	body	320	valid
19.0ms	124×	body	80	valid
15.0ms	148×	body	80	nan
9.0ms	11×	body	640	nan
4.0ms	10×	body	320	nan
4.0ms	14×	body	160	valid
3.0ms	8×	body	160	nan

simplify1.4s

Counts: 1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize32.0ms

Local error

Found 3 expressions with local error:

1.9b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.7b	(pow (+ x 1) (/ 1 n))
0.5b	(pow x (/ 1 n))

rewrite135.0ms

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

113.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
13.0ms	(pow (+ x 1) (/ 1 n))
5.0ms	(pow x (/ 1 n))

series445.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

248.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
138.0ms	(pow (+ x 1) (/ 1 n))
59.0ms	(pow x (/ 1 n))

simplify703.0ms

Counts: 161 → 161

prune1.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.3b

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
1.9b	(log (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))
0.7b	(pow (+ 1 x) (/ 1 n))
0.5b	(pow x (/ 1 n))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 241

Calls

4 calls:

Slowest

126.0ms	(log (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))
61.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
9.0ms	(pow (+ 1 x) (/ 1 n))
4.0ms	(pow x (/ 1 n))

series688.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

261.0ms	(log (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))
256.0ms	(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
99.0ms	(pow (+ 1 x) (/ 1 n))
71.0ms	(pow x (/ 1 n))

simplify960.0ms

Counts: 253 → 253

prune3.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.2b

localize20.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (exp (* (/ 1 n) (log1p x))) (pow x (/ 1 n)))
1.9b	(log (exp (- (exp (* (/ 1 n) (log1p x))) (pow x (/ 1 n)))))
0.5b	(pow x (/ 1 n))
0.3b	(* (/ 1 n) (log1p x))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
49×	`add-cube-cbrt`
42×	`prod-diff`
26×	`log-prod`
23×	`unpow-prod-down` `exp-sum`
20×	`times-frac`
14×	`add-exp-log`
13×	`pow-unpow` `associate-l`
9×	`add-cbrt-cube` `sqr-pow`
8×	`pow1` `log-pow`
7×	`exp-prod`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `unswap-sqr`
2×	`sub-neg` `div-exp` `cbrt-unprod` `div-inv` `distribute-lft-out--`
1×	`pow-to-exp` `cbrt-undiv` `log-div` `rec-exp` `pow-pow` `flip3--` `exp-diff` `diff-log` `1-exp` `rem-log-exp` `pow-prod-down` `associate-l/` `pow-exp` `-commutative` `flip--`

Counts

4 → 157

Calls

4 calls:

Slowest

70.0ms	(log (exp (- (exp (* (/ 1 n) (log1p x))) (pow x (/ 1 n)))))
22.0ms	(* (/ 1 n) (log1p x))
19.0ms	(- (exp (* (/ 1 n) (log1p x))) (pow x (/ 1 n)))
5.0ms	(pow x (/ 1 n))

series549.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

193.0ms	(- (exp (* (/ 1 n) (log1p x))) (pow x (/ 1 n)))
192.0ms	(log (exp (- (exp (* (/ 1 n) (log1p x))) (pow x (/ 1 n)))))
90.0ms	(pow x (/ 1 n))
73.0ms	(* (/ 1 n) (log1p x))

simplify818.0ms

Counts: 169 → 169

prune2.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 16.0b

localize62.0ms

Local error

Found 4 expressions with local error:

7.3b	(* n (* x x))
6.7b	(* (* n n) x)
3.5b	(- (/ (/ 1 n) x) (/ 1/2 (* n (* x x))))
0.5b	(/ 1/2 (* n (* x x)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

666×	`times-frac`
388×	`add-sqr-sqrt`
378×	`*-un-lft-identity`
374×	`add-cube-cbrt`
301×	`prod-diff`
77×	`div-inv`
43×	`fma-neg`
23×	`add-cbrt-cube` `add-exp-log`
14×	`pow1`
9×	`prod-exp` `cbrt-unprod`
6×	`pow-prod-down` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`*-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 436

Calls

4 calls:

Slowest

47.0ms	(- (/ (/ 1 n) x) (/ 1/2 (* n (* x x))))
37.0ms	(* (* n n) x)
27.0ms	(* n (* x x))
12.0ms	(/ 1/2 (* n (* x x)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

75.0ms	(- (/ (/ 1 n) x) (/ 1/2 (* n (* x x))))
36.0ms	(/ 1/2 (* n (* x x)))
32.0ms	(* n (* x x))
18.0ms	(* (* n n) x)

simplify914.0ms

Counts: 448 → 448

prune6.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 15.9b

regimes385.0ms

Accuracy

86.3% (1.7b remaining)

Error of 18.9b against oracle of 17.1b and baseline of 29.7b

bsearch499.0ms

end0.0ms

sample10.5s

Algorithm

intervals

Results

3.1s	3166×	body	1280	valid
1.8s	1624×	body	640	valid
1.2s	1115×	body	10240	exit
996.0ms	4715×	body	80	valid
859.0ms	833×	body	320	valid
702.0ms	672×	body	1280	nan
547.0ms	4953×	body	80	nan
429.0ms	614×	body	640	nan
173.0ms	334×	body	320	nan
166.0ms	476×	body	160	valid
82.0ms	185×	body	160	nan