Details

sample294.0ms

Algorithm

intervals

Results

105.0ms	109×	body	1280	valid
35.0ms	50×	body	640	valid
22.0ms	35×	body	10240	exit
21.0ms	164×	body	80	valid
19.0ms	22×	body	1280	nan
15.0ms	20×	body	640	nan
13.0ms	165×	body	80	nan
12.0ms	26×	body	320	valid
4.0ms	11×	body	320	nan
3.0ms	13×	body	160	valid
1.0ms	2×	body	160	nan

simplify1.7s

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize18.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(pow (+ x 1.0) (/ 1.0 n))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

70×	`unpow-prod-down`
67×	`*-un-lft-identity`
56×	`prod-diff`
54×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
23×	`sqr-pow`
13×	`pow-unpow`
10×	`distribute-lft-out`
9×	`times-frac` `difference-of-squares`
8×	`fma-neg`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `div-inv` `flip--`

Counts

2 → 120

Calls

2 calls:

151.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))

series625.0ms

Counts

2 → 6

Calls

2 calls:

374.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
251.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify1.5s

Counts

126 → 126

Iterations

Iter	Nodes
done	5002
2	2229
1	600
0	233

prune470.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.7b	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
1.7b	(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
3.3b	(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))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
28×	`cbrt-prod` `add-cube-cbrt`
26×	`pow-unpow`
20×	`pow1`
18×	`times-frac`
13×	`pow1/3`
12×	`cbrt-div`
11×	`pow-pow`
10×	`add-exp-log`
9×	`swap-sqr`
8×	`unpow-prod-down`
7×	`associate-r` `associate-l` `distribute-lft-out`
6×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `pow-prod-down` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-exp`
2×	`pow2` `pow-to-exp` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `div-inv` `sqr-pow`
1×	`*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 135

Calls

4 calls:

41.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
16.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
26.0ms	(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)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

series2.4s

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
473.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
525.0ms	(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
1.3s	(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))))

simplify2.1s

Counts

147 → 147

Iterations

Iter	Nodes
done	5001
2	4232
1	898
0	303

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.5b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.7b	(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
3.8b	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (fma (/ -1/3 (/ n (- (log x)))) 1.0 (+ 1 (/ (/ 0.3333333333333333 n) x))) (- (pow x (/ 1.0 n))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
28×	`cbrt-prod` `add-sqr-sqrt`
20×	`add-cube-cbrt`
19×	`pow1`
14×	`cbrt-div`
13×	`pow-unpow` `pow1/3`
9×	`pow-pow` `times-frac` `swap-sqr` `add-exp-log`
7×	`flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `pow-prod-down` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow2` `pow-plus` `associate-l/` `pow-exp` `prod-exp` `associate-r/`
1×	`pow-to-exp` `unpow-prod-down` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `sqr-pow`

Counts

4 → 117

Calls

4 calls:

6.0ms	(cbrt (+ x 1.0))
59.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
37.0ms	(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 (/ -1/3 (/ n (- (log x)))) 1.0 (+ 1 (/ (/ 0.3333333333333333 n) x))) (- (pow x (/ 1.0 n))))

series1.5s

Counts

4 → 12

Calls

4 calls:

104.0ms	(cbrt (+ x 1.0))
151.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
465.0ms	(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
788.0ms	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (fma (/ -1/3 (/ n (- (log x)))) 1.0 (+ 1 (/ (/ 0.3333333333333333 n) x))) (- (pow x (/ 1.0 n))))

simplify1.5s

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
2	3688
1	828
0	297

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.5b

localize90.0ms

Local error

Found 4 expressions with local error:

2.3b	(cbrt (- (* (pow (pow (sqrt (cbrt (+ x 1.0))) (+ 3 1)) (/ 1.0 n)) (+ (fma (/ -1/3 n) (* (- (log x)) 1.0) 1) (/ 0.3333333333333333 (* n x)))) (pow x (/ 1.0 n))))
3.8b	(- (* (pow (pow (sqrt (cbrt (+ x 1.0))) (+ 3 1)) (/ 1.0 n)) (+ (fma (/ -1/3 n) (* (- (log x)) 1.0) 1) (/ 0.3333333333333333 (* n x)))) (pow x (/ 1.0 n)))
3.8b	(- (* (pow (pow (sqrt (cbrt (+ x 1.0))) (+ 3 1)) (/ 1.0 n)) (+ (fma (/ -1/3 n) (* (- (log x)) 1.0) 1) (/ 0.3333333333333333 (* n x)))) (pow x (/ 1.0 n)))
3.8b	(- (* (pow (pow (sqrt (cbrt (+ x 1.0))) (+ 3 1)) (/ 1.0 n)) (+ (fma (/ -1/3 n) (* (- (log x)) 1.0) 1) (/ 0.3333333333333333 (* n x)))) (pow x (/ 1.0 n)))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

21×	`prod-diff`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`add-log-exp`
9×	`unpow-prod-down`
6×	`associate--l+`
4×	`expm1-log1p-u` `pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--`
3×	`cbrt-prod` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `fma-neg` `diff-log` `sqr-pow`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 87

Calls

4 calls:

52.0ms	(cbrt (- (* (pow (pow (sqrt (cbrt (+ x 1.0))) (+ 3 1)) (/ 1.0 n)) (+ (fma (/ -1/3 n) (* (- (log x)) 1.0) 1) (/ 0.3333333333333333 (* n x)))) (pow x (/ 1.0 n))))
49.0ms	(- (* (pow (pow (sqrt (cbrt (+ x 1.0))) (+ 3 1)) (/ 1.0 n)) (+ (fma (/ -1/3 n) (* (- (log x)) 1.0) 1) (/ 0.3333333333333333 (* n x)))) (pow x (/ 1.0 n)))
55.0ms	(- (* (pow (pow (sqrt (cbrt (+ x 1.0))) (+ 3 1)) (/ 1.0 n)) (+ (fma (/ -1/3 n) (* (- (log x)) 1.0) 1) (/ 0.3333333333333333 (* n x)))) (pow x (/ 1.0 n)))
48.0ms	(- (* (pow (pow (sqrt (cbrt (+ x 1.0))) (+ 3 1)) (/ 1.0 n)) (+ (fma (/ -1/3 n) (* (- (log x)) 1.0) 1) (/ 0.3333333333333333 (* n x)))) (pow x (/ 1.0 n)))

series5.7s

Counts

4 → 12

Calls

4 calls:

2.0s	(cbrt (- (* (pow (pow (sqrt (cbrt (+ x 1.0))) (+ 3 1)) (/ 1.0 n)) (+ (fma (/ -1/3 n) (* (- (log x)) 1.0) 1) (/ 0.3333333333333333 (* n x)))) (pow x (/ 1.0 n))))
1.3s	(- (* (pow (pow (sqrt (cbrt (+ x 1.0))) (+ 3 1)) (/ 1.0 n)) (+ (fma (/ -1/3 n) (* (- (log x)) 1.0) 1) (/ 0.3333333333333333 (* n x)))) (pow x (/ 1.0 n)))
1.2s	(- (* (pow (pow (sqrt (cbrt (+ x 1.0))) (+ 3 1)) (/ 1.0 n)) (+ (fma (/ -1/3 n) (* (- (log x)) 1.0) 1) (/ 0.3333333333333333 (* n x)))) (pow x (/ 1.0 n)))
1.2s	(- (* (pow (pow (sqrt (cbrt (+ x 1.0))) (+ 3 1)) (/ 1.0 n)) (+ (fma (/ -1/3 n) (* (- (log x)) 1.0) 1) (/ 0.3333333333333333 (* n x)))) (pow x (/ 1.0 n)))

simplify1.7s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	3978
1	888
0	304

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.5b

regimes673.0ms

Accuracy

79.3% (1.9b remaining)

Error of 22.4b against oracle of 20.5b and baseline of 29.5b

bsearch4.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	39
1	39
0	32

end0.0ms

sample8.6s

Algorithm

intervals

Results

2.6s	3114×	body	1280	valid
1.0s	1633×	body	640	valid
919.0ms	4699×	body	80	valid
857.0ms	1155×	body	10240	exit
778.0ms	653×	body	640	nan
551.0ms	592×	body	1280	nan
435.0ms	836×	body	320	valid
326.0ms	5042×	body	80	nan
161.0ms	471×	body	160	valid
103.0ms	323×	body	320	nan
86.0ms	208×	body	160	nan