Details

sample90.0ms

Algorithm

intervals

Results

20.0ms	303×	body	80	nan
17.0ms	56×	body	640	valid
12.0ms	30×	body	1280	valid
12.0ms	19×	body	320	valid
11.0ms	135×	body	80	valid
3.0ms	16×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	13
0	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
4.8b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite94.0ms

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:

5.0ms	(sqrt (+ x 1))
9.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))
43.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series156.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt (+ x 1))
30.0ms	(/ 1 (sqrt (+ x 1)))
34.0ms	(/ 1 (sqrt x))
67.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify2.4s

Counts

805 → 805

Iterations

Iter	Nodes
done	5000
2	2463
1	1435
0	651

prune1.9s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 19.4b

localize81.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
28.7b	(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))))))))
32.6b	(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)))))))

rewrite4.0ms

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))))))))
1.0ms	(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)))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

294.0ms	(cbrt x)
269.0ms	(cbrt x)
182.0ms	(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))))))))
331.0ms	(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)))))))

simplify2.1s

Counts

62 → 62

Iterations

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

prune642.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 19.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
10.8b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite53.0ms

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:

5.0ms	(sqrt (+ x 1))
9.0ms	(/ 1 (sqrt (+ x 1)))
26.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series180.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(sqrt (+ x 1))
45.0ms	(/ 1 (sqrt (+ x 1)))
103.0ms	(- (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

prune778.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 19.3b

localize86.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
28.7b	(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))))))))
28.7b	(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))))))))
32.6b	(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)))))))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 47

Calls

4 calls:

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) (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)))))))

series659.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(cbrt x)
111.0ms	(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))))))))
113.0ms	(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))))))))
222.0ms	(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)))))))

simplify1.6s

Counts

59 → 59

Iterations

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

prune587.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 19.3b

regimes179.0ms

Accuracy

0% (1.2b remaining)

Error of 20.5b against oracle of 19.3b and baseline of 20.5b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	47
4	47
3	45
2	39
1	32
0	22

end0.0ms

sample2.9s

Algorithm

intervals

Results

958.0ms	1814×	body	640	valid
560.0ms	8149×	body	80	nan
534.0ms	1120×	body	1280	valid
410.0ms	4131×	body	80	valid
184.0ms	621×	body	320	valid
70.0ms	314×	body	160	valid