Details

sample55.0ms

Algorithm

intervals

Results

11.0ms	71×	body	640	valid
10.0ms	282×	body	80	nan
8.0ms	38×	body	1280	valid
5.0ms	123×	body	80	valid
2.0ms	18×	body	320	valid
0.0ms	6×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
1.5b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
879×	`*-un-lft-identity`
747×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
566×	`sqrt-prod`
74×	`distribute-lft-out`
54×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `hypot-def` `flip--`

Counts

4 → 758

Calls

4 calls:

12.0ms	(sqrt (+ x 1.0))
20.0ms	(/ 1.0 (sqrt (+ x 1.0)))
15.0ms	(/ 1.0 (sqrt x))
122.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series427.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (+ x 1.0))
125.0ms	(/ 1.0 (sqrt (+ x 1.0)))
50.0ms	(/ 1.0 (sqrt x))
199.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.9s

Counts

770 → 770

Iterations

Iter	Nodes
done	5000
2	4935
1	1587
0	702

prune3.2s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 20.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt x))
0.2b	(/ 1.0 (sqrt x))
1.5b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
1.5b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite318.0ms

Algorithm

rewrite-expression-head

Rules

2028×	`times-frac`
1700×	`*-un-lft-identity`
1450×	`add-sqr-sqrt`
1390×	`add-cube-cbrt`
1188×	`prod-diff`
1092×	`sqrt-prod`
138×	`distribute-lft-out`
106×	`div-inv`
88×	`sqrt-div` `associate-/r/`
44×	`flip3-+` `fma-neg` `flip-+`
22×	`distribute-lft-out--`
18×	`difference-of-squares`
12×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `frac-sub` `flip--`

Counts

4 → 1384

Calls

4 calls:

5.0ms	(/ 1.0 (sqrt x))
5.0ms	(/ 1.0 (sqrt x))
84.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
78.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1.0 (sqrt x))
45.0ms	(/ 1.0 (sqrt x))
186.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
180.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.7s

Counts

1396 → 1396

Iterations

Iter	Nodes
done	5000
2	4595
1	1526
0	674

prune6.8s

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 20.4b

localize138.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1.0 (sqrt x)))
1.5b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
31.9b	(fma (* (cbrt (/ 1.0 (sqrt x))) (cbrt (/ 1.0 (sqrt x)))) (cbrt (/ 1.0 (sqrt x))) (- (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (cbrt (/ 1.0 (sqrt (+ x 1.0))))))))
33.0b	(fma (- (cbrt (/ 1.0 (sqrt (+ x 1.0))))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (cbrt (/ 1.0 (sqrt (+ x 1.0))))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (cbrt (/ 1.0 (sqrt (+ x 1.0)))))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

1014×	`times-frac`
850×	`*-un-lft-identity`
725×	`add-sqr-sqrt`
695×	`add-cube-cbrt`
594×	`prod-diff`
543×	`sqrt-prod`
69×	`distribute-lft-out`
53×	`div-inv`
44×	`sqrt-div` `associate-/r/`
22×	`cbrt-prod` `flip3-+` `fma-neg` `flip-+`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
2×	`fma-udef`
1×	`cbrt-div` `sub-neg` `flip3--` `pow1/3` `diff-log` `frac-sub` `flip--`

Counts

4 → 704

Calls

4 calls:

3.0ms	(cbrt (/ 1.0 (sqrt x)))
70.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
0.0ms	(fma (* (cbrt (/ 1.0 (sqrt x))) (cbrt (/ 1.0 (sqrt x)))) (cbrt (/ 1.0 (sqrt x))) (- (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (cbrt (/ 1.0 (sqrt (+ x 1.0))))))))
0.0ms	(fma (- (cbrt (/ 1.0 (sqrt (+ x 1.0))))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (cbrt (/ 1.0 (sqrt (+ x 1.0))))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (cbrt (/ 1.0 (sqrt (+ x 1.0)))))))

series1.7s

Counts

4 → 12

Calls

4 calls:

252.0ms	(cbrt (/ 1.0 (sqrt x)))
142.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
374.0ms	(fma (* (cbrt (/ 1.0 (sqrt x))) (cbrt (/ 1.0 (sqrt x)))) (cbrt (/ 1.0 (sqrt x))) (- (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (cbrt (/ 1.0 (sqrt (+ x 1.0))))))))
906.0ms	(fma (- (cbrt (/ 1.0 (sqrt (+ x 1.0))))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (cbrt (/ 1.0 (sqrt (+ x 1.0))))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (* (cbrt (/ 1.0 (sqrt (+ x 1.0)))) (cbrt (/ 1.0 (sqrt (+ x 1.0)))))))

simplify2.0s

Counts

716 → 716

Iterations

Iter	Nodes
done	5000
1	1859
0	810

prune4.0s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 20.4b

localize101.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
31.9b	(fma (/ 1 (sqrt (* (cbrt x) (cbrt x)))) (/ 1.0 (sqrt (cbrt x))) (- (* (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (/ 1 (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))))))
33.0b	(fma (- (/ 1.0 (sqrt (cbrt (+ x 1.0))))) (/ 1 (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (* (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (/ 1 (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))))))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`

Counts

4 → 46

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
0.0ms	(fma (/ 1 (sqrt (* (cbrt x) (cbrt x)))) (/ 1.0 (sqrt (cbrt x))) (- (* (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (/ 1 (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))))))
0.0ms	(fma (- (/ 1.0 (sqrt (cbrt (+ x 1.0))))) (/ 1 (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (* (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (/ 1 (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

188.0ms	(cbrt x)
184.0ms	(cbrt x)
156.0ms	(fma (/ 1 (sqrt (* (cbrt x) (cbrt x)))) (/ 1.0 (sqrt (cbrt x))) (- (* (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (/ 1 (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))))))
655.0ms	(fma (- (/ 1.0 (sqrt (cbrt (+ x 1.0))))) (/ 1 (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (* (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (/ 1 (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))))))

simplify1.2s

Counts

58 → 58

Iterations

Iter	Nodes
done	5001
2	1848
1	466
0	178

prune366.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.3b

regimes125.0ms

Accuracy

91.5% (0.6b remaining)

Error of 19.9b against oracle of 19.3b and baseline of 26.2b

bsearch48.0ms

Steps

Iters	Range		Point
7	1.229414737037e+78	1.4867452701985317e+80	9.993638768580709e+79

simplify15.0ms

Iterations

Iter	Nodes
done	31
1	31
0	26

end0.0ms

sample1.5s

Algorithm

intervals

Results

409.0ms	4058×	body	80	valid
312.0ms	7994×	body	80	nan
308.0ms	1872×	body	640	valid
186.0ms	1130×	body	1280	valid
106.0ms	629×	body	320	valid
19.0ms	311×	body	160	valid