Details

sample191.0ms

Algorithm

intervals

Results

51.0ms	94×	body	1280	valid
30.0ms	47×	body	10240	exit
27.0ms	65×	body	640	valid
13.0ms	16×	body	1280	nan
10.0ms	144×	body	80	valid
10.0ms	23×	body	640	nan
8.0ms	178×	body	80	nan
6.0ms	25×	body	320	valid
3.0ms	15×	body	160	valid
2.0ms	7×	body	320	nan
1.0ms	8×	body	160	nan

simplify1.0s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite142.0ms

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))
19.0ms	(pow (+ x 1.0) (/ 1.0 n))
115.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series797.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(pow x (/ 1.0 n))
254.0ms	(pow (+ x 1.0) (/ 1.0 n))
462.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.3s

Counts

88 → 88

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	190	1337
1	546	1246
2	2100	1206
done	5000	1204

prune452.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.5b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite343.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
27×	`unpow-prod-down`
26×	`pow-unpow`
22×	`add-cube-cbrt`
18×	`times-frac` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
14×	`sqr-pow`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube`
3×	`distribute-lft-out`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 109

Calls

4 calls:

7.0ms	(pow x (/ 1.0 n))
21.0ms	(pow (+ x 1.0) (/ 1.0 n))
193.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
114.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

88.0ms	(pow x (/ 1.0 n))
214.0ms	(pow (+ x 1.0) (/ 1.0 n))
439.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
396.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.4s

Counts

121 → 121

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	235	1971
1	631	1802
2	2336	1714
done	5001	1712

prune588.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.8b

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
2.0b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (* (* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n)))))))
2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n)))))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow-unpow`
24×	`*-un-lft-identity`
22×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
7×	`pow1` `unpow-prod-down`
6×	`add-exp-log` `add-log-exp`
5×	`log-prod`
4×	`log-pow` `add-cbrt-cube`
3×	`exp-prod`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `div-inv` `sqr-pow`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out`

Counts

4 → 85

Calls

4 calls:

11.0ms	(pow x (/ 1.0 n))
20.0ms	(pow (+ x 1.0) (/ 1.0 n))
162.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (* (* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n)))))))
132.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

75.0ms	(pow x (/ 1.0 n))
199.0ms	(pow (+ x 1.0) (/ 1.0 n))
466.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (* (* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n)))))))
426.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n)))))

simplify1.3s

Counts

97 → 97

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	200	2119
1	577	1977
2	2301	1249
done	5001	1247

prune619.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.8b

localize40.0ms

Local error

Found 4 expressions with local error:

1.3b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.3b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite480.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`unpow-prod-down`
18×	`difference-of-squares`
16×	`log-prod`
12×	`sqr-pow`
10×	`cbrt-prod`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`sub-neg` `exp-sum` `log-pow` `add-cbrt-cube`
2×	`log-div` `cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

103.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
120.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
125.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
129.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series2.6s

Counts

4 → 12

Calls

4 calls:

1.1s	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
679.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
415.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
419.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify620.0ms

Counts

98 → 98

Iterations

Useful iterations: done (616.0ms)

Iter	Nodes	Cost
0	141	2446
1	305	2374
2	951	2196
done	5000	2156

prune679.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.7b

regimes402.0ms

Accuracy

78.2% (1.8b remaining)

Error of 22.4b against oracle of 20.5b and baseline of 29.0b

bsearch3.0ms

simplify22.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	44	121
1	54	121
2	58	121
3	61	121
done	61	121

end0.0ms

sample8.5s

Algorithm

intervals

Results

2.9s	3179×	body	1280	valid
1.4s	1549×	body	640	valid
1.1s	1149×	body	10240	exit
594.0ms	627×	body	1280	nan
479.0ms	4725×	body	80	valid
418.0ms	4983×	body	80	nan
353.0ms	620×	body	640	nan
341.0ms	846×	body	320	valid
145.0ms	452×	body	160	valid
95.0ms	297×	body	320	nan
35.0ms	182×	body	160	nan