Details

sample231.0ms

Algorithm

intervals

Results

88.0ms	108×	body	1280	valid
21.0ms	23×	body	1280	nan
19.0ms	34×	body	640	valid
16.0ms	30×	body	10240	exit
16.0ms	164×	body	80	valid
10.0ms	150×	body	80	nan
9.0ms	14×	body	640	nan
9.0ms	24×	body	320	valid
4.0ms	10×	body	320	nan
4.0ms	13×	body	160	valid
2.0ms	8×	body	160	nan

simplify2.4s

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize51.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite157.0ms

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:

9.0ms	(pow x (/ 1.0 n))
22.0ms	(pow (+ x 1.0) (/ 1.0 n))
121.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series705.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(pow x (/ 1.0 n))
202.0ms	(pow (+ x 1.0) (/ 1.0 n))
428.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify711.0ms

Counts: 88 → 88

prune400.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
0.3b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.3b	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
47×	`unpow-prod-down`
46×	`cbrt-prod`
33×	`*-un-lft-identity`
27×	`difference-of-squares`
26×	`pow-unpow`
25×	`add-cube-cbrt`
23×	`sqr-pow`
18×	`times-frac`
17×	`cube-prod`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube`
3×	`distribute-lft-out`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`cube-mult` `sub-neg` `flip3--` `pow1/3` `diff-log` `unpow3` `flip--` `rem-cbrt-cube` `distribute-lft-out--`

Counts

4 → 126

Calls

4 calls:

18.0ms	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
5.0ms	(pow x (/ 1.0 n))
21.0ms	(pow (+ x 1.0) (/ 1.0 n))
246.0ms	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

series867.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
74.0ms	(pow x (/ 1.0 n))
198.0ms	(pow (+ x 1.0) (/ 1.0 n))
387.0ms	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

simplify811.0ms

Counts: 138 → 138

prune614.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.5b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite405.0ms

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:

4.0ms	(pow x (/ 1.0 n))
14.0ms	(pow (+ x 1.0) (/ 1.0 n))
98.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
285.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

89.0ms	(pow x (/ 1.0 n))
198.0ms	(pow (+ x 1.0) (/ 1.0 n))
443.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
448.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify780.0ms

Counts: 121 → 121

prune548.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 17.5b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite399.0ms

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:

101.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
126.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
75.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
91.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series2.2s

Counts

4 → 12

Calls

4 calls:

410.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
450.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
701.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
682.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify1.5s

Counts: 98 → 98

prune607.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 17.5b

regimes467.0ms

Accuracy

84.2% (1.4b remaining)

Error of 21.7b against oracle of 20.3b and baseline of 29.4b

bsearch220.0ms

Steps

Iters	Range		Point
9	1958959.7701095298	435146901375.54236	28958019.028174132
6	-380908646326105.1	-24837594819674.312	-27546108091290.383

simplify959.0ms

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.5s	3143×	body	1280	valid
1.7s	1582×	body	640	valid
762.0ms	1143×	body	10240	exit
493.0ms	642×	body	1280	nan
474.0ms	4757×	body	80	valid
387.0ms	4974×	body	80	nan
364.0ms	647×	body	640	nan
336.0ms	845×	body	320	valid
195.0ms	431×	body	160	valid
105.0ms	340×	body	320	nan
38.0ms	208×	body	160	nan