Details

sample219.0ms

Algorithm

intervals

Results

76.0ms	107×	body	1280	valid
22.0ms	39×	body	640	valid
20.0ms	20×	body	1280	nan
15.0ms	30×	body	10240	exit
13.0ms	149×	body	80	valid
12.0ms	26×	body	640	nan
11.0ms	173×	body	80	nan
11.0ms	35×	body	320	valid
5.0ms	15×	body	320	nan
3.0ms	15×	body	160	valid
1.0ms	3×	body	160	nan

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	34	13
3	81	13
4	238	13
5	1224	13
done	5000	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.3b	(pow (+ x 1.0) (/ 1.0 n))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

5.0ms	(pow x (/ 1.0 n))
145.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))

series751.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(pow x (/ 1.0 n))
391.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
281.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify1.2s

Counts

88 → 88

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	190	1337
1	546	1246
2	2105	1206
done	5001	1204

prune430.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow x (/ (/ 1.0 n) 2))
1.2b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
1.3b	(pow (+ x 1.0) (/ 1.0 n))
1.3b	(pow (+ x 1.0) (/ 1.0 n))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
73×	`add-sqr-sqrt`
69×	`pow-unpow`
62×	`*-un-lft-identity`
56×	`add-cube-cbrt`
18×	`unpow-prod-down`
12×	`difference-of-squares`
10×	`sqr-pow`
9×	`sqrt-prod`
7×	`pow1` `add-exp-log`
6×	`div-inv` `add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `pow-exp`
2×	`distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 138

Calls

4 calls:

8.0ms	(pow x (/ (/ 1.0 n) 2))
101.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
16.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.1s

Counts

4 → 12

Calls

4 calls:

93.0ms	(pow x (/ (/ 1.0 n) 2))
590.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
209.0ms	(pow (+ x 1.0) (/ 1.0 n))
223.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify2.6s

Counts

150 → 150

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	279	2303
1	887	2115
2	3688	2045
done	5001	2045

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.1b

localize70.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (/ 0.5 (* x n)) (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (- (log x)) (* x (pow n 2))))))
3.0b	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (- (/ 0.5 (* x n)) (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (- (log x)) (* x (pow n 2)))))))
9.4b	(* x (pow n 2))
9.9b	(* (pow x 2) n)

rewrite418.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
17×	`associate-*r/`
16×	`add-exp-log`
15×	`associate-l`
14×	`-un-lft-identity` `associate-r*`
12×	`add-cube-cbrt` `frac-sub`
10×	`frac-times` `flip3-+` `add-cbrt-cube` `flip-+`
9×	`unswap-sqr`
8×	`unpow-prod-down`
7×	`prod-exp`
6×	`pow1` `add-log-exp`
4×	`flip3--` `frac-add` `flip--` `unpow2` `sqr-pow`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `*-commutative` `cbrt-unprod`
2×	`pow-to-exp` `associate-*l/` `pow-exp` `associate--r+`
1×	`diff-log` `pow-prod-down` `distribute-lft-out`

Counts

4 → 111

Calls

4 calls:

45.0ms	(- (/ 0.5 (* x n)) (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (- (log x)) (* x (pow n 2))))))
337.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (- (/ 0.5 (* x n)) (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (- (log x)) (* x (pow n 2)))))))
12.0ms	(* x (pow n 2))
13.0ms	(* (pow x 2) n)

series1.0s

Counts

4 → 12

Calls

4 calls:

141.0ms	(- (/ 0.5 (* x n)) (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (- (log x)) (* x (pow n 2))))))
813.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (- (/ 0.5 (* x n)) (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (- (log x)) (* x (pow n 2)))))))
48.0ms	(* x (pow n 2))
38.0ms	(* (pow x 2) n)

simplify566.0ms

Counts

123 → 123

Iterations

Useful iterations: done (558.0ms)

Iter	Nodes	Cost
0	283	4800
1	895	4422
done	5000	4065

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 18.0b

localize76.0ms

Local error

Found 4 expressions with local error:

3.0b	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (- (/ 0.5 (* x n)) (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (- (log x)) (exp (log (* x (pow n 2)))))))))
9.4b	(* x (pow n 2))
9.9b	(* (pow x 2) n)
28.6b	(log (* x (pow n 2)))

rewrite437.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`add-exp-log`
15×	`associate-l`
14×	`-un-lft-identity` `associate-r/` `associate-r`
12×	`add-cube-cbrt`
10×	`frac-times` `prod-exp` `add-cbrt-cube`
9×	`flip3-+` `frac-sub` `flip-+` `unswap-sqr`
8×	`unpow-prod-down`
7×	`pow1`
4×	`rem-log-exp` `unpow2` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `flip3--` `frac-add` `pow-exp` `*-commutative` `flip--` `cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`
1×	`log-prod` `pow-prod-down` `log-pow` `distribute-lft-out`

Counts

4 → 107

Calls

4 calls:

390.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (- (/ 0.5 (* x n)) (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (- (log x)) (exp (log (* x (pow n 2)))))))))
12.0ms	(* x (pow n 2))
23.0ms	(* (pow x 2) n)
8.0ms	(log (* x (pow n 2)))

series978.0ms

Counts

4 → 12

Calls

4 calls:

809.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (- (/ 0.5 (* x n)) (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (- (log x)) (exp (log (* x (pow n 2)))))))))
59.0ms	(* x (pow n 2))
36.0ms	(* (pow x 2) n)
73.0ms	(log (* x (pow n 2)))

simplify594.0ms

Counts

119 → 119

Iterations

Useful iterations: done (586.0ms)

Iter	Nodes	Cost
0	282	4171
1	855	3668
done	5000	3330

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 18.0b

regimes420.0ms

Accuracy

80% (1.7b remaining)

Error of 22.2b against oracle of 20.5b and baseline of 28.9b

bsearch312.0ms

Steps

Iters	Range		Point
10	1821600688.6938446	1.479248585578744e+22	11998314702.36214
6	-4.224272091334773e+22	-3.0644814537608586e+21	-3.1349534972691606e+21

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	131
1	66	131
done	66	131

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.1s	3214×	body	1280	valid
1.4s	1483×	body	640	valid
969.0ms	1131×	body	10240	exit
581.0ms	692×	body	1280	nan
530.0ms	4751×	body	80	valid
444.0ms	678×	body	640	nan
441.0ms	5076×	body	80	nan
314.0ms	821×	body	320	valid
145.0ms	475×	body	160	valid
137.0ms	381×	body	320	nan
34.0ms	174×	body	160	nan