Details

sample78.0ms

Algorithm

intervals

Results

25.0ms	64×	body	640	valid
13.0ms	248×	body	80	nan
11.0ms	33×	body	1280	valid
9.0ms	132×	body	80	valid
4.0ms	20×	body	320	valid
1.0ms	7×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	13
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
1.9b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

1063×	`times-frac`
902×	`*-un-lft-identity`
788×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
580×	`sqrt-prod`
74×	`distribute-lft-out`
56×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
25×	`difference-of-squares`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*` `distribute-lft-out--`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube`
6×	`pow-flip` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `hypot-def` `inv-pow`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 793

Calls

4 calls:

13.0ms	(sqrt (+ x 1))
23.0ms	(/ 1 (sqrt (+ x 1)))
15.0ms	(/ 1 (sqrt x))
137.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series184.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ x 1))
42.0ms	(/ 1 (sqrt (+ x 1)))
38.0ms	(/ 1 (sqrt x))
73.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify2.0s

Counts

805 → 805

Iterations

Iter	Nodes
done	5000
2	2463
1	1435
0	651

prune1.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 19.8b

localize84.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
29.6b	(fma (/ (sqrt 1) (sqrt (* (cbrt x) (cbrt x)))) (/ (sqrt 1) (sqrt (cbrt x))) (- (* (/ (sqrt 1) (sqrt (cbrt (+ x 1)))) (/ (sqrt 1) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))
31.8b	(fma (- (/ (sqrt 1) (sqrt (cbrt (+ x 1))))) (/ (sqrt 1) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (/ (sqrt 1) (sqrt (cbrt (+ x 1)))) (/ (sqrt 1) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))))

rewrite3.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`

Counts

4 → 50

Calls

4 calls:

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

series863.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(cbrt x)
257.0ms	(cbrt x)
119.0ms	(fma (/ (sqrt 1) (sqrt (* (cbrt x) (cbrt x)))) (/ (sqrt 1) (sqrt (cbrt x))) (- (* (/ (sqrt 1) (sqrt (cbrt (+ x 1)))) (/ (sqrt 1) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))
255.0ms	(fma (- (/ (sqrt 1) (sqrt (cbrt (+ x 1))))) (/ (sqrt 1) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (/ (sqrt 1) (sqrt (cbrt (+ x 1)))) (/ (sqrt 1) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))))

simplify2.5s

Counts

62 → 62

Iterations

Iter	Nodes
done	5002
3	2518
2	760
1	266
0	115

prune467.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 19.7b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
10.5b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

236×	`*-un-lft-identity`
209×	`add-sqr-sqrt`
189×	`prod-diff`
180×	`times-frac`
174×	`add-cube-cbrt`
110×	`sqrt-prod`
89×	`unpow-prod-down`
33×	`sqr-pow`
26×	`distribute-lft-out`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`difference-of-squares`
9×	`flip3-+` `flip-+` `div-inv`
7×	`associate-/r*` `fma-neg` `add-exp-log`
6×	`pow1`
5×	`add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `pow-flip` `associate-/l*`
2×	`sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `1-exp` `flip--` `inv-pow`

Counts

3 → 303

Calls

3 calls:

7.0ms	(sqrt (+ x 1))
13.0ms	(/ 1 (sqrt (+ x 1)))
47.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series118.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(sqrt (+ x 1))
29.0ms	(/ 1 (sqrt (+ x 1)))
64.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify2.0s

Counts

312 → 312

Iterations

Iter	Nodes
done	5000
3	4518
2	1883
1	949
0	401

prune692.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 19.7b

localize72.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
29.5b	(fma (pow (* (cbrt x) (cbrt x)) -1/2) (pow (cbrt x) -1/2) (- (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))
31.8b	(fma (- (/ 1 (sqrt (cbrt (+ x 1))))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))))

rewrite3.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`

Counts

4 → 50

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
0.0ms	(fma (pow (* (cbrt x) (cbrt x)) -1/2) (pow (cbrt x) -1/2) (- (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))
0.0ms	(fma (- (/ 1 (sqrt (cbrt (+ x 1))))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))))

series767.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(cbrt x)
202.0ms	(cbrt x)
153.0ms	(fma (pow (* (cbrt x) (cbrt x)) -1/2) (pow (cbrt x) -1/2) (- (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))
212.0ms	(fma (- (/ 1 (sqrt (cbrt (+ x 1))))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))))

simplify1.6s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
3	2462
2	748
1	267
0	114

prune367.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 19.7b

regimes111.0ms

Accuracy

80% (0.7b remaining)

Error of 19.3b against oracle of 18.7b and baseline of 22.0b

bsearch68.0ms

Steps

Iters	Range		Point
8	1.5529870713201007e+199	1.232441400819276e+202	8.343787893268626e+200

simplify3.0ms

Iterations

Iter	Nodes
done	25
1	25
0	20

end0.0ms

sample1.6s

Algorithm

intervals

Results

560.0ms	1781×	body	640	valid
410.0ms	8127×	body	80	nan
219.0ms	1115×	body	1280	valid
185.0ms	4167×	body	80	valid
91.0ms	629×	body	320	valid
21.0ms	308×	body	160	valid