Details

sample93.0ms

Algorithm

intervals

Results

32.0ms	64×	body	640	valid
17.0ms	267×	body	80	nan
15.0ms	36×	body	1280	valid
9.0ms	116×	body	80	valid
6.0ms	28×	body	320	valid
2.0ms	12×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	17
2	17
1	13
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
3.4b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite110.0ms

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:

7.0ms	(sqrt (+ x 1))
16.0ms	(/ 1 (sqrt (+ x 1)))
9.0ms	(/ 1 (sqrt x))
55.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ x 1))
33.0ms	(/ 1 (sqrt (+ x 1)))
35.0ms	(/ 1 (sqrt x))
91.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify916.0ms

Counts

805 → 805

Iterations

Iter	Nodes
2	2402
1	1415
0	651

prune7.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 20.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt x) 1)
0.2b	(/ 1 (hypot (sqrt x) 1))
0.2b	(/ 1 (sqrt x))
3.4b	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

rewrite42.0ms

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))
5.0ms	(/ 1 (sqrt x))
23.0ms	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

series804.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(hypot (sqrt x) 1)
254.0ms	(/ 1 (hypot (sqrt x) 1))
30.0ms	(/ 1 (sqrt x))
334.0ms	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

simplify694.0ms

Counts

451 → 451

Iterations

Iter	Nodes
2	2270
1	1130
0	495

prune3.6s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 20.5b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
10.4b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite46.0ms

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))))

series123.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(sqrt (+ x 1))
33.0ms	(/ 1 (sqrt (+ x 1)))
62.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify1.1s

Counts

312 → 312

Iterations

Iter	Nodes
3	3667
2	1693
1	931
0	401

prune2.6s

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 20.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow x -1/2) (sqrt (+ x 1)))
0.3b	(fma (pow x -1/2) (pow x -1/2) (/ (pow x -1/2) (sqrt (+ x 1))))
10.5b	(- (/ (pow x -1/2) x) (/ (/ 1 (+ x 1)) (sqrt (+ x 1))))
13.8b	(/ (- (/ (pow x -1/2) x) (/ (/ 1 (+ x 1)) (sqrt (+ x 1)))) (+ (/ 1 (+ x 1)) (fma (pow x -1/2) (pow x -1/2) (/ (pow x -1/2) (sqrt (+ x 1))))))

rewrite408.0ms

Algorithm

rewrite-expression-head

Rules

8717×	`times-frac`
6454×	`*-un-lft-identity`
4978×	`add-sqr-sqrt`
4264×	`add-cube-cbrt`
3300×	`prod-diff`
1916×	`sqrt-prod`
1270×	`unpow-prod-down`
1053×	`distribute-lft-out`
456×	`sqr-pow`
404×	`associate-/r/`
377×	`div-inv`
202×	`flip3-+` `flip-+`
196×	`difference-of-squares`
52×	`sqrt-div`
41×	`associate-/l*`
25×	`fma-neg`
21×	`distribute-lft-out--`
12×	`associate-/r*`
11×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `frac-sub` `flip--`
1×	`pow-to-exp` `sub-neg` `diff-log` `div-sub` `pow-exp` `fma-udef`

Counts

4 → 3695

Calls

4 calls:

11.0ms	(/ (pow x -1/2) (sqrt (+ x 1)))
0.0ms	(fma (pow x -1/2) (pow x -1/2) (/ (pow x -1/2) (sqrt (+ x 1))))
43.0ms	(- (/ (pow x -1/2) x) (/ (/ 1 (+ x 1)) (sqrt (+ x 1))))
161.0ms	(/ (- (/ (pow x -1/2) x) (/ (/ 1 (+ x 1)) (sqrt (+ x 1)))) (+ (/ 1 (+ x 1)) (fma (pow x -1/2) (pow x -1/2) (/ (pow x -1/2) (sqrt (+ x 1))))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (pow x -1/2) (sqrt (+ x 1)))
90.0ms	(fma (pow x -1/2) (pow x -1/2) (/ (pow x -1/2) (sqrt (+ x 1))))
83.0ms	(- (/ (pow x -1/2) x) (/ (/ 1 (+ x 1)) (sqrt (+ x 1))))
210.0ms	(/ (- (/ (pow x -1/2) x) (/ (/ 1 (+ x 1)) (sqrt (+ x 1)))) (+ (/ 1 (+ x 1)) (fma (pow x -1/2) (pow x -1/2) (/ (pow x -1/2) (sqrt (+ x 1))))))

simplify4.4s

Counts

3707 → 3707

Iterations

Iter	Nodes
1	6264
0	2831

prune46.2s

Pruning

44 alts after pruning (43 fresh and 1 done)

Merged error: 20.0b

regimes322.0ms

Accuracy

0% (0.9b remaining)

Error of 19.5b against oracle of 18.6b and baseline of 19.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	9
1	9
0	7

end0.0ms

sample1.9s

Algorithm

intervals

Results

504.0ms	1878×	body	640	valid
438.0ms	8102×	body	80	nan
421.0ms	1147×	body	1280	valid
248.0ms	4060×	body	80	valid
137.0ms	603×	body	320	valid
34.0ms	312×	body	160	valid