Details

sample292.0ms

Algorithm

intervals

Results

91.0ms	88×	body	1280	valid
56.0ms	45×	body	10240	exit
31.0ms	52×	body	640	valid
20.0ms	162×	body	80	valid
19.0ms	29×	body	640	nan
16.0ms	183×	body	80	nan
13.0ms	27×	body	320	valid
11.0ms	13×	body	1280	nan
7.0ms	23×	body	160	valid
5.0ms	10×	body	320	nan
2.0ms	7×	body	160	nan

simplify299.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

299.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize21.0ms

Local error

Found 3 expressions with local error:

3.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.2b	(pow (+ x 1) (/ 1 n))
0.8b	(pow x (/ 1 n))

rewrite71.0ms

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

59.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
7.0ms	(pow (+ x 1) (/ 1 n))
3.0ms	(pow x (/ 1 n))

series473.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

276.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
113.0ms	(pow (+ x 1) (/ 1 n))
84.0ms	(pow x (/ 1 n))

simplify41.0s

Counts

188 → 161

Calls

188 calls:

Slowest

944.0ms	(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
584.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
563.0ms	(+ (sqrt (pow (+ x 1) (/ 1 n))) (pow (sqrt x) (/ 1 n)))
545.0ms	(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
542.0ms	(- (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: 19.0b

localize55.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.2b	(pow (+ x 1) (/ 1 n))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

202×	`unpow-prod-down`
179×	`*-un-lft-identity`
168×	`prod-diff`
144×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
67×	`sqr-pow`
28×	`distribute-lft-out`
27×	`difference-of-squares`
24×	`fma-neg`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 304

Calls

4 calls:

Slowest

81.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
55.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
55.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
12.0ms	(pow (+ x 1) (/ 1 n))

series881.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

271.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
268.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
256.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
86.0ms	(pow (+ x 1) (/ 1 n))

simplify1.9m

Counts

460 → 316

Calls

460 calls:

Slowest

700.0ms	(fma (- (sqrt (pow x (/ 1 n)))) (sqrt (pow x (/ 1 n))) (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n)))))
681.0ms	(fma (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
665.0ms	(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
611.0ms	(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
601.0ms	(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))

prune4.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.0b

localize23.0ms

Local error

Found 4 expressions with local error:

3.5b	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
3.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.2b	(pow (+ x 1) (/ 1 n))
0.8b	(pow x (/ 1 n))

rewrite242.0ms

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

129.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
88.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
12.0ms	(pow (+ x 1) (/ 1 n))
5.0ms	(pow x (/ 1 n))

series715.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

282.0ms	(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
251.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
108.0ms	(pow (+ x 1) (/ 1 n))
74.0ms	(pow x (/ 1 n))

simplify1.1m

Counts

269 → 253

Calls

269 calls:

Slowest

787.0ms	(fma (- (sqrt (pow x (/ 1 n)))) (sqrt (pow x (/ 1 n))) (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n)))))
636.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
609.0ms	(log (exp (fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))))
541.0ms	(+ (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
523.0ms	(+ (sqrt (pow (+ x 1) (/ 1 n))) (pow (sqrt x) (/ 1 n)))

prune3.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.0b

localize65.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.4b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.0b	(log (exp (* (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))) (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

198×	`unpow-prod-down`
170×	`*-un-lft-identity`
168×	`prod-diff`
137×	`add-sqr-sqrt`
101×	`add-cube-cbrt`
66×	`sqr-pow`
27×	`distribute-lft-out` `difference-of-squares`
24×	`fma-neg`
11×	`add-log-exp`
9×	`distribute-lft-out--`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `sub-neg` `flip3--` `diff-log` `log-pow` `flip--`
1×	`exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 290

Calls

4 calls:

Slowest

90.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
70.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
70.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.0ms	(log (exp (* (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))) (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

Slowest

825.0ms	(log (exp (* (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))) (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))))
244.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
238.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
231.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.4m

Counts

447 → 302

Calls

447 calls:

Slowest

781.0ms	(fma (- (sqrt (pow x (/ 1 n)))) (sqrt (pow x (/ 1 n))) (* (sqrt (pow x (/ 1 n))) (sqrt (pow x (/ 1 n)))))
652.0ms	(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
581.0ms	(- (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))
445.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (cbrt (pow x (/ 1 n))) (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))))))
414.0ms	(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

prune3.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.0b

regimes287.0ms

Accuracy

88% (1.3b remaining)

Error of 19.2b against oracle of 17.9b and baseline of 29.0b

bsearch306.0ms

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.5s	3143×	body	1280	valid
919.0ms	1183×	body	10240	exit
885.0ms	1553×	body	640	valid
805.0ms	4752×	body	80	valid
488.0ms	608×	body	1280	nan
384.0ms	5201×	body	80	nan
371.0ms	650×	body	640	nan
330.0ms	885×	body	320	valid
117.0ms	378×	body	320	nan
97.0ms	452×	body	160	valid
35.0ms	189×	body	160	nan