Details

sample675.0ms

Algorithm

intervals

Results

351.0ms	59×	body	640	valid
104.0ms	103×	body	1280	valid
37.0ms	28×	body	1280	nan
32.0ms	39×	body	10240	exit
22.0ms	140×	body	80	valid
18.0ms	189×	body	80	nan
15.0ms	25×	body	640	nan
8.0ms	18×	body	320	valid
8.0ms	7×	body	320	nan
4.0ms	13×	body	160	valid
2.0ms	8×	body	160	nan

simplify11.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3081
5	667
4	238
3	86
2	35
1	17
0	8

prune73.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize55.0ms

Local error

Found 3 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.1b	(pow (+ x 1.0) (/ 1.0 n))

rewrite543.0ms

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:

12.0ms	(pow x (/ 1.0 n))
492.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
20.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.5s

Counts

3 → 9

Calls

3 calls:

138.0ms	(pow x (/ 1.0 n))
824.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
581.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify10.9s

Counts

158 → 158

Iterations

Iter	Nodes
done	5001
2	1905
1	716
0	271

prune3.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.6b

localize132.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1.0 n))
0.8b	(pow x (/ 1.0 n))
1.4b	(pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
1.5b	(- (pow (pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))) (pow x (/ 1.0 n)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

156×	`unpow-prod-down`
88×	`*-un-lft-identity`
87×	`add-sqr-sqrt`
84×	`prod-diff`
68×	`add-cube-cbrt`
41×	`sqr-pow`
18×	`times-frac`
15×	`difference-of-squares`
14×	`pow-unpow`
13×	`cbrt-prod`
12×	`fma-neg`
9×	`distribute-lft-out`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `cbrt-div` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 197

Calls

4 calls:

10.0ms	(cbrt (/ 1.0 n))
63.0ms	(pow x (/ 1.0 n))
58.0ms	(pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
987.0ms	(- (pow (pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))) (pow x (/ 1.0 n)))

series5.4s

Counts

4 → 12

Calls

4 calls:

951.0ms	(cbrt (/ 1.0 n))
260.0ms	(pow x (/ 1.0 n))
1.2s	(pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
2.9s	(- (pow (pow (+ x 1.0) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n))) (pow x (/ 1.0 n)))

simplify9.0s

Counts

209 → 209

Iterations

Iter	Nodes
done	5004
2	2968
1	1053
0	423

prune5.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.5b

localize91.0ms

Local error

Found 4 expressions with local error:

1.1b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
4.8b	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
34×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
12×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out` `sqr-pow`
1×	`fma-udef`

Counts

4 → 100

Calls

4 calls:

37.0ms	(pow (+ x 1.0) (/ 1.0 n))
210.0ms	(pow (+ x 1.0) (/ 1.0 n))
19.0ms	(pow (+ x 1.0) (/ 1.0 n))
1.0ms	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

series6.3s

Counts

4 → 12

Calls

4 calls:

617.0ms	(pow (+ x 1.0) (/ 1.0 n))
871.0ms	(pow (+ x 1.0) (/ 1.0 n))
487.0ms	(pow (+ x 1.0) (/ 1.0 n))
4.3s	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

simplify9.3s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
3	3183
2	972
1	355
0	129

prune3.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.4b

localize83.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.0b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.1b	(pow (+ x 1.0) (/ 1.0 n))

rewrite843.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 237

Calls

4 calls:

8.0ms	(pow x (/ 1.0 n))
481.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
303.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
20.0ms	(pow (+ x 1.0) (/ 1.0 n))

series3.7s

Counts

4 → 12

Calls

4 calls:

683.0ms	(pow x (/ 1.0 n))
1.3s	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
596.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.2s	(pow (+ x 1.0) (/ 1.0 n))

simplify7.2s

Counts

249 → 249

Iterations

Iter	Nodes
done	5002
2	2218
1	903
0	430

prune3.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.4b

regimes930.0ms

Accuracy

83.4% (1.5b remaining)

Error of 22.0b against oracle of 20.6b and baseline of 29.3b

bsearch706.0ms

Steps

Iters	Range		Point
7	0.6307682633451466	37.746059492850215	37.00630601379255
10	-88176342586.65536	-1.963203309137196e-05	-24784678.57450563

simplify29.0ms

Iterations

Iter	Nodes
done	59
1	59
0	47

end4.0ms

sample32.5s

Algorithm

intervals

Results

14.5s	3166×	body	1280	valid
3.6s	1154×	body	10240	exit
3.0s	1586×	body	640	valid
2.1s	4669×	body	80	valid
2.1s	625×	body	1280	nan
1.8s	5030×	body	80	nan
1.7s	317×	body	320	nan
1.5s	634×	body	640	nan
647.0ms	871×	body	320	valid
233.0ms	462×	body	160	valid
85.0ms	202×	body	160	nan