Details

sample284.0ms

Algorithm

intervals

Results

90.0ms	104×	body	1280	valid
37.0ms	53×	body	640	valid
31.0ms	33×	body	10240	exit
16.0ms	22×	body	640	nan
15.0ms	130×	body	80	valid
14.0ms	17×	body	1280	nan
14.0ms	173×	body	80	nan
12.0ms	24×	body	320	valid
6.0ms	13×	body	320	nan
5.0ms	15×	body	160	valid
2.0ms	7×	body	160	nan

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	35	13
3	86	13
4	252	13
5	1266	13
done	5000	13

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite209.0ms

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:

7.0ms	(pow x (/ 1.0 n))
19.0ms	(pow (+ x 1.0) (/ 1.0 n))
171.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series855.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(pow x (/ 1.0 n))
244.0ms	(pow (+ x 1.0) (/ 1.0 n))
484.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.6s

Counts

158 → 158

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	271	4785
1	740	3759
2	2874	3021
done	5002	2906

prune999.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.1b

localize113.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.0b	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
2.7b	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`pow-unpow`
10×	`cbrt-prod`
9×	`times-frac`
7×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `fma-udef` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

1.0ms	(cbrt x)
2.0ms	(cbrt x)
23.0ms	(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 (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

series3.6s

Counts

4 → 12

Calls

4 calls:

353.0ms	(cbrt x)
363.0ms	(cbrt x)
626.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
2.3s	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

simplify2.0s

Counts

82 → 82

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	220	1410
1	634	1304
2	2782	1160
done	5002	1150

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.0b

localize103.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.0b	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
2.7b	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))
10.2b	(log (exp (cbrt x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
17×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`pow-unpow`
10×	`cbrt-prod`
9×	`times-frac`
7×	`unpow-prod-down` `log-pow`
6×	`pow1` `exp-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod`
2×	`pow-pow` `pow1/3`
1×	`pow-to-exp` `rem-log-exp` `pow-exp` `fma-udef` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

1.0ms	(cbrt x)
31.0ms	(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 (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))
8.0ms	(log (exp (cbrt x)))

series3.1s

Counts

4 → 12

Calls

4 calls:

320.0ms	(cbrt x)
535.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
1.9s	(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))
354.0ms	(log (exp (cbrt x)))

simplify2.0s

Counts

89 → 89

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	249	1484
1	672	1337
2	2876	1190
done	5000	1180

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 20.0b

localize150.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (- (log x)) (pow n 2))
1.7b	(fma (/ -1/3 (pow n 2)) (/ (- (log x)) x) (fma (/ -2/3 x) (/ (- (log x)) (pow n 2)) (/ 1 (* x n))))
3.4b	(fma (/ -2/3 x) (/ (- (log x)) (pow n 2)) (/ 1 (* x n)))
8.1b	(* (pow x 2) n)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
66×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
43×	`unpow-prod-down`
36×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
22×	`pow1`
18×	`log-pow`
15×	`unpow2` `sqr-pow`
14×	`add-exp-log`
12×	`associate-/l*`
9×	`neg-mul-1`
8×	`associate-l` `associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`div-exp` `associate-r` `prod-exp`
2×	`pow-to-exp` `pow-exp` `fma-udef`
1×	`cbrt-undiv` `neg-sub0` `frac-2neg` `div-sub` `distribute-frac-neg` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 183

Calls

4 calls:

28.0ms	(/ (- (log x)) (pow n 2))
1.0ms	(fma (/ -1/3 (pow n 2)) (/ (- (log x)) x) (fma (/ -2/3 x) (/ (- (log x)) (pow n 2)) (/ 1 (* x n))))
1.0ms	(fma (/ -2/3 x) (/ (- (log x)) (pow n 2)) (/ 1 (* x n)))
24.0ms	(* (pow x 2) n)

series647.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (- (log x)) (pow n 2))
184.0ms	(fma (/ -1/3 (pow n 2)) (/ (- (log x)) x) (fma (/ -2/3 x) (/ (- (log x)) (pow n 2)) (/ 1 (* x n))))
276.0ms	(fma (/ -2/3 x) (/ (- (log x)) (pow n 2)) (/ 1 (* x n)))
39.0ms	(* (pow x 2) n)

simplify2.8s

Counts

195 → 195

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	279	2860
1	598	2663
2	3072	2320
done	5001	2316

prune2.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 19.9b

regimes633.0ms

Accuracy

76.4% (2.0b remaining)

Error of 22.7b against oracle of 20.6b and baseline of 29.3b

bsearch3.0ms

simplify20.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	58	171
1	79	171
2	81	171
done	81	171

end0.0ms

sample11.0s

Algorithm

intervals

Results

3.6s	3186×	body	1280	valid
1.1s	1552×	body	640	valid
1.1s	1166×	body	10240	exit
1.1s	4952×	body	80	nan
781.0ms	4757×	body	80	valid
752.0ms	653×	body	1280	nan
678.0ms	680×	body	640	nan
436.0ms	865×	body	320	valid
149.0ms	364×	body	320	nan
122.0ms	438×	body	160	valid
84.0ms	191×	body	160	nan