Details

sample315.0ms

Algorithm

intervals

Results

122.0ms	96×	body	1280	valid
46.0ms	48×	body	640	valid
25.0ms	154×	body	80	valid
23.0ms	27×	body	10240	exit
23.0ms	22×	body	1280	nan
15.0ms	26×	body	320	valid
14.0ms	122×	body	80	nan
13.0ms	17×	body	640	nan
6.0ms	17×	body	160	valid
3.0ms	6×	body	320	nan
1.0ms	3×	body	160	nan

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2099
6	2099
5	1210
4	275
3	89
2	37
1	19
0	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize19.0ms

Local error

Found 3 expressions with local error:

1.0b	(pow x (/ 1 n))
1.2b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.2b	(pow (+ x 1) (/ 1 n))

rewrite123.0ms

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:

6.0ms	(pow x (/ 1 n))
105.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
7.0ms	(pow (+ x 1) (/ 1 n))

series436.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(pow x (/ 1 n))
238.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
142.0ms	(pow (+ x 1) (/ 1 n))

simplify1.5s

Counts

161 → 161

Iterations

Iter	Nodes
done	2000
3	2000
2	1672
1	653
0	257

prune777.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.2b

localize112.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (cbrt x) (/ 1 n))
1.2b	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
1.5b	(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)))))
2.2b	(pow (cbrt (+ x 1)) (/ 1 n))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
31×	`*-un-lft-identity`
29×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
14×	`pow1` `unpow-prod-down`
13×	`pow-pow`
9×	`add-exp-log`
8×	`pow1/3`
7×	`cbrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `div-inv` `sqr-pow`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `fma-udef` `distribute-lft-out`

Counts

4 → 117

Calls

4 calls:

4.0ms	(pow (cbrt x) (/ 1 n))
14.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
0.0ms	(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)))))
14.0ms	(pow (cbrt (+ x 1)) (/ 1 n))

series1.4s

Counts

4 → 12

Calls

4 calls:

156.0ms	(pow (cbrt x) (/ 1 n))
199.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
880.0ms	(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)))))
195.0ms	(pow (cbrt (+ x 1)) (/ 1 n))

simplify1.7s

Counts

129 → 129

Iterations

Iter	Nodes
done	2001
2	2001
1	816
0	274

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.0b

localize124.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
1.3b	(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)))))))
1.5b	(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)))))
2.2b	(pow (cbrt (+ x 1)) (/ 1 n))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow-unpow`
24×	`*-un-lft-identity`
22×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
14×	`pow1`
11×	`pow-pow`
8×	`unpow-prod-down` `add-exp-log`
7×	`pow1/3`
4×	`cbrt-prod` `expm1-log1p-u` `log-prod` `add-cbrt-cube` `log-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-prod` `pow-exp`
2×	`pow-to-exp` `pow-prod-down` `pow-sqr` `pow-prod-up` `fma-udef` `div-inv` `sqr-pow`
1×	`pow2` `pow-plus` `rem-log-exp` `exp-sum` `prod-exp` `distribute-lft-out`

Counts

4 → 102

Calls

4 calls:

20.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
4.0ms	(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)))))))
0.0ms	(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)))))
13.0ms	(pow (cbrt (+ x 1)) (/ 1 n))

series2.0s

Counts

4 → 12

Calls

4 calls:

187.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
815.0ms	(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)))))))
803.0ms	(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)))))
194.0ms	(pow (cbrt (+ x 1)) (/ 1 n))

simplify1.5s

Counts

114 → 114

Iterations

Iter	Nodes
done	2000
2	2000
1	720
0	259

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (log1p x) (/ 1 n))
1.0b	(pow x (/ 1 n))
1.2b	(- (exp (* (log1p x) (/ 1 n))) (pow x (/ 1 n)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
33×	`add-cube-cbrt`
21×	`prod-diff`
20×	`times-frac`
13×	`pow-unpow` `unpow-prod-down` `associate-r` `add-exp-log`
8×	`add-cbrt-cube`
6×	`pow1`
5×	`add-log-exp` `sqr-pow`
4×	`prod-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-l` `insert-posit16` `log1p-expm1-u` `difference-of-squares` `unswap-sqr`
2×	`div-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `cbrt-undiv` `rec-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `1-exp` `pow-prod-down` `pow-exp` `associate-r/` `un-div-inv` `-commutative` `flip--` `distribute-lft-out--`

Counts

3 → 112

Calls

3 calls:

10.0ms	(* (log1p x) (/ 1 n))
8.0ms	(pow x (/ 1 n))
18.0ms	(- (exp (* (log1p x) (/ 1 n))) (pow x (/ 1 n)))

series428.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(* (log1p x) (/ 1 n))
68.0ms	(pow x (/ 1 n))
260.0ms	(- (exp (* (log1p x) (/ 1 n))) (pow x (/ 1 n)))

simplify1.5s

Counts

121 → 121

Iterations

Iter	Nodes
done	2001
3	2001
2	1776
1	657
0	253

prune562.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 14.8b

regimes406.0ms

Accuracy

80.7% (2.3b remaining)

Error of 19.9b against oracle of 17.6b and baseline of 29.5b

bsearch621.0ms

Steps

Iters	Range		Point
10	0.1386194397507998	38953256569.61001	590284494.5165114
9	-9.999093156786688e-301	-1.919784781288074e-306	-1.9461952197688902e-306
8	-1.5101531889076583e+43	-5.4185333785510155e+38	-5.516643619668029e+38

simplify33.0ms

Iterations

Iter	Nodes
done	109
4	109
3	106
2	100
1	87
0	65

end0.0ms

sample11.4s

Algorithm

intervals

Results

3.9s	3107×	body	1280	valid
1.5s	1662×	body	640	valid
1.4s	1166×	body	10240	exit
1.1s	5040×	body	80	nan
774.0ms	617×	body	1280	nan
770.0ms	4735×	body	80	valid
575.0ms	651×	body	640	nan
539.0ms	858×	body	320	valid
159.0ms	324×	body	320	nan
147.0ms	444×	body	160	valid
57.0ms	193×	body	160	nan