Details

sample263.0ms

Algorithm

intervals

Results

75.0ms	90×	body	1280	valid
37.0ms	31×	body	10240	exit
30.0ms	16×	body	1280	nan
25.0ms	43×	body	640	valid
16.0ms	169×	body	80	valid
15.0ms	170×	body	80	nan
15.0ms	24×	body	640	nan
11.0ms	29×	body	320	valid
3.0ms	15×	body	160	valid
3.0ms	10×	body	320	nan
1.0ms	6×	body	160	nan

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1264
4	252
3	86
2	35
1	17
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite131.0ms

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` `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 → 149

Calls

3 calls:

4.0ms	(pow x (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
111.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series766.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(pow x (/ 1.0 n))
259.0ms	(pow (+ x 1.0) (/ 1.0 n))
409.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.6s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	2866
1	738
0	270

prune682.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.5b	(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
0.7b	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
3.2b	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow-unpow`
25×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
13×	`pow1`
11×	`pow-pow`
8×	`cbrt-prod` `unpow-prod-down` `pow1/3` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-exp`
2×	`pow-to-exp` `cbrt-div` `pow-prod-down` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out` `sqr-pow`
1×	`pow2` `flip3-+` `pow-plus` `prod-exp` `flip-+` `fma-udef`

Counts

4 → 96

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
18.0ms	(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
8.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
1.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

series2.6s

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt (+ x 1.0))
848.0ms	(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
466.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
1.2s	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

simplify1.7s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
2	3541
1	836
0	279

prune884.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.6b

localize83.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.5b	(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
1.8b	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (fma 1.0 (/ -1/3 (/ n (- (log x)))) (+ 1 (/ (/ 0.3333333333333333 x) n))) (- (pow x (/ 1.0 n))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `pow-unpow` `add-cube-cbrt`
12×	`pow1`
9×	`pow-pow` `times-frac`
8×	`cbrt-prod` `pow1/3`
7×	`add-exp-log`
4×	`expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `pow-prod-down` `pow-exp` `pow-sqr` `pow-prod-up` `flip-+` `distribute-lft-out`
1×	`pow2` `pow-to-exp` `unpow-prod-down` `pow-plus` `prod-exp` `fma-udef` `div-inv` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

6.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
20.0ms	(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
1.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (fma 1.0 (/ -1/3 (/ n (- (log x)))) (+ 1 (/ (/ 0.3333333333333333 x) n))) (- (pow x (/ 1.0 n))))

series1.5s

Counts

4 → 12

Calls

4 calls:

114.0ms	(cbrt (+ x 1.0))
132.0ms	(cbrt (+ x 1.0))
507.0ms	(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
717.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (fma 1.0 (/ -1/3 (/ n (- (log x)))) (+ 1 (/ (/ 0.3333333333333333 x) n))) (- (pow x (/ 1.0 n))))

simplify1.1s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	2753
1	685
0	243

prune799.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.6b

localize73.0ms

Local error

Found 4 expressions with local error:

1.8b	(fma (+ (fma (* 1.0 (/ -1/3 n)) (- (log x)) (/ 0.3333333333333333 (* n x))) 1) (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
2.0b	(cbrt (fma (+ (fma (* 1.0 (/ -1/3 n)) (- (log x)) (/ 0.3333333333333333 (* n x))) 1) (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (- (pow x (/ 1.0 n)))))
2.0b	(cbrt (fma (+ (fma (* 1.0 (/ -1/3 n)) (- (log x)) (/ 0.3333333333333333 (* n x))) 1) (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (- (pow x (/ 1.0 n)))))
2.0b	(cbrt (fma (+ (fma (* 1.0 (/ -1/3 n)) (- (log x)) (/ 0.3333333333333333 (* n x))) 1) (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (- (pow x (/ 1.0 n)))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(fma (+ (fma (* 1.0 (/ -1/3 n)) (- (log x)) (/ 0.3333333333333333 (* n x))) 1) (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
1.0ms	(cbrt (fma (+ (fma (* 1.0 (/ -1/3 n)) (- (log x)) (/ 0.3333333333333333 (* n x))) 1) (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (- (pow x (/ 1.0 n)))))
1.0ms	(cbrt (fma (+ (fma (* 1.0 (/ -1/3 n)) (- (log x)) (/ 0.3333333333333333 (* n x))) 1) (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (- (pow x (/ 1.0 n)))))
2.0ms	(cbrt (fma (+ (fma (* 1.0 (/ -1/3 n)) (- (log x)) (/ 0.3333333333333333 (* n x))) 1) (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (- (pow x (/ 1.0 n)))))

series3.1s

Counts

4 → 12

Calls

4 calls:

350.0ms	(fma (+ (fma (* 1.0 (/ -1/3 n)) (- (log x)) (/ 0.3333333333333333 (* n x))) 1) (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
931.0ms	(cbrt (fma (+ (fma (* 1.0 (/ -1/3 n)) (- (log x)) (/ 0.3333333333333333 (* n x))) 1) (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (- (pow x (/ 1.0 n)))))
876.0ms	(cbrt (fma (+ (fma (* 1.0 (/ -1/3 n)) (- (log x)) (/ 0.3333333333333333 (* n x))) 1) (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (- (pow x (/ 1.0 n)))))
895.0ms	(cbrt (fma (+ (fma (* 1.0 (/ -1/3 n)) (- (log x)) (/ 0.3333333333333333 (* n x))) 1) (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (- (pow x (/ 1.0 n)))))

simplify1.3s

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
2	2959
1	675
0	225

prune881.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 20.6b

regimes661.0ms

Accuracy

83.2% (1.5b remaining)

Error of 21.9b against oracle of 20.4b and baseline of 29.5b

bsearch2.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	40
2	40
1	38
0	32

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.5s	3137×	body	1280	valid
1.1s	672×	body	1280	nan
989.0ms	4706×	body	80	valid
981.0ms	1624×	body	640	valid
899.0ms	1151×	body	10240	exit
547.0ms	633×	body	640	nan
355.0ms	848×	body	320	valid
330.0ms	5096×	body	80	nan
156.0ms	316×	body	320	nan
97.0ms	441×	body	160	valid
36.0ms	182×	body	160	nan