Details

sample124.0ms

Algorithm

intervals

Results

36.0ms	271×	body	80	nan
32.0ms	71×	body	640	valid
17.0ms	29×	body	1280	valid
15.0ms	132×	body	80	valid
5.0ms	14×	body	320	valid
2.0ms	10×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	15
2	15
1	11
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
2.5b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite124.0ms

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))
16.0ms	(/ 1 (sqrt (+ x 1)))
11.0ms	(/ 1 (sqrt x))
62.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series228.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ x 1))
38.0ms	(/ 1 (sqrt (+ x 1)))
50.0ms	(/ 1 (sqrt x))
98.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify3.3s

Counts

805 → 805

Iterations

Iter	Nodes
2	2418
1	1414
0	651

prune8.9s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 19.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt x) 1)
0.1b	(/ 1 (hypot (sqrt x) 1))
0.3b	(/ 1 (sqrt x))
2.5b	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

505×	`times-frac`
406×	`add-sqr-sqrt`
386×	`*-un-lft-identity`
365×	`add-cube-cbrt`
286×	`prod-diff`
144×	`sqrt-prod`
42×	`div-inv`
22×	`fma-neg`
15×	`difference-of-squares`
12×	`add-exp-log`
9×	`associate-/r*`
8×	`add-cbrt-cube`
7×	`pow1` `distribute-lft-out--`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `pow-flip`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `inv-pow`
1×	`hypot-udef` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 439

Calls

4 calls:

0.0ms	(hypot (sqrt x) 1)
4.0ms	(/ 1 (hypot (sqrt x) 1))
10.0ms	(/ 1 (sqrt x))
25.0ms	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

series1.1s

Counts

4 → 12

Calls

4 calls:

234.0ms	(hypot (sqrt x) 1)
378.0ms	(/ 1 (hypot (sqrt x) 1))
39.0ms	(/ 1 (sqrt x))
474.0ms	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

simplify2.5s

Counts

451 → 451

Iterations

Iter	Nodes
2	2272
1	1129
0	495

prune5.3s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 19.1b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
8.5b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite66.0ms

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:

9.0ms	(sqrt (+ x 1))
9.0ms	(/ 1 (sqrt (+ x 1)))
33.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series139.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(sqrt (+ x 1))
40.0ms	(/ 1 (sqrt (+ x 1)))
64.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify2.9s

Counts

312 → 312

Iterations

Iter	Nodes
3	3597
2	1677
1	930
0	401

prune2.9s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 19.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt x))
0.6b	(cbrt (sqrt x))
29.4b	(fma (* (/ 1 (cbrt (sqrt x))) (/ 1 (cbrt (sqrt x)))) (/ 1 (cbrt (sqrt x))) (/ (/ -1 (sqrt (cbrt (+ x 1)))) (fabs (cbrt (+ x 1)))))
32.6b	(fma (/ -1 (sqrt (cbrt (+ x 1)))) (/ 1 (fabs (cbrt (+ x 1)))) (/ (/ 1 (fabs (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-prod`
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 → 56

Calls

4 calls:

7.0ms	(cbrt (sqrt x))
1.0ms	(cbrt (sqrt x))
0.0ms	(fma (* (/ 1 (cbrt (sqrt x))) (/ 1 (cbrt (sqrt x)))) (/ 1 (cbrt (sqrt x))) (/ (/ -1 (sqrt (cbrt (+ x 1)))) (fabs (cbrt (+ x 1)))))
0.0ms	(fma (/ -1 (sqrt (cbrt (+ x 1)))) (/ 1 (fabs (cbrt (+ x 1)))) (/ (/ 1 (fabs (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

209.0ms	(cbrt (sqrt x))
202.0ms	(cbrt (sqrt x))
269.0ms	(fma (* (/ 1 (cbrt (sqrt x))) (/ 1 (cbrt (sqrt x)))) (/ 1 (cbrt (sqrt x))) (/ (/ -1 (sqrt (cbrt (+ x 1)))) (fabs (cbrt (+ x 1)))))
512.0ms	(fma (/ -1 (sqrt (cbrt (+ x 1)))) (/ 1 (fabs (cbrt (+ x 1)))) (/ (/ 1 (fabs (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))))

simplify1.8s

Counts

68 → 68

Iterations

Iter	Nodes
3	2892
2	850
1	306
0	133

prune825.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 19.1b

regimes174.0ms

Accuracy

0% (0.6b remaining)

Error of 19.7b against oracle of 19.1b and baseline of 19.7b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
1	7
0	7

end0.0ms

sample2.9s

Algorithm

intervals

Results

678.0ms	8041×	body	80	nan
638.0ms	4103×	body	80	valid
625.0ms	1848×	body	640	valid
472.0ms	1161×	body	1280	valid
160.0ms	596×	body	320	valid
97.0ms	292×	body	160	valid