Details

sample114.0ms

Algorithm

intervals

Results

30.0ms	52×	body	1280	valid
23.0ms	235×	body	80	nan
19.0ms	43×	body	640	valid
15.0ms	131×	body	80	valid
9.0ms	27×	body	320	valid
1.0ms	3×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	13
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
1.1b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite144.0ms

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:

10.0ms	(sqrt (+ x 1))
18.0ms	(/ 1 (sqrt (+ x 1)))
10.0ms	(/ 1 (sqrt x))
58.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (+ x 1))
49.0ms	(/ 1 (sqrt (+ x 1)))
52.0ms	(/ 1 (sqrt x))
126.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify1.4s

Counts

805 → 805

Iterations

Iter	Nodes
done	2000
2	2000
1	1435
0	651

prune2.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 17.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (/ 1 (sqrt (+ x 1)))))
0.2b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
1.1b	(- (/ 1 (sqrt x)) (expm1 (log1p (/ 1 (sqrt (+ x 1))))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

122×	`*-un-lft-identity`
121×	`add-sqr-sqrt`
115×	`times-frac`
109×	`add-cube-cbrt`
66×	`prod-diff` `sqrt-prod`
22×	`fma-neg`
13×	`associate-/r*`
12×	`add-exp-log`
8×	`pow1` `add-cbrt-cube`
7×	`div-inv`
6×	`pow-flip` `associate-/l*` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `1-exp` `associate-/r/` `distribute-lft-out--` `inv-pow` `expm1-udef`
1×	`expm1-log1p` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--` `associate--r-`

Counts

4 → 225

Calls

4 calls:

0.0ms	(expm1 (log1p (/ 1 (sqrt (+ x 1)))))
18.0ms	(/ 1 (sqrt (+ x 1)))
10.0ms	(/ 1 (sqrt x))
26.0ms	(- (/ 1 (sqrt x)) (expm1 (log1p (/ 1 (sqrt (+ x 1))))))

series564.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(expm1 (log1p (/ 1 (sqrt (+ x 1)))))
49.0ms	(/ 1 (sqrt (+ x 1)))
54.0ms	(/ 1 (sqrt x))
244.0ms	(- (/ 1 (sqrt x)) (expm1 (log1p (/ 1 (sqrt (+ x 1))))))

simplify1.0s

Counts

237 → 237

Iterations

Iter	Nodes
done	2005
3	2005
2	1055
1	517
0	262

prune775.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 17.9b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
10.9b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite60.0ms

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

series147.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(sqrt (+ x 1))
37.0ms	(/ 1 (sqrt (+ x 1)))
72.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify1.4s

Counts

312 → 312

Iterations

Iter	Nodes
done	2003
3	2003
2	1883
1	949
0	401

prune1.3s

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 17.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
0.5b	(* (pow x -1/2) (pow x -1/2))
0.8b	(/ (- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (pow x -1/2) (/ 1 (sqrt (+ x 1)))))
9.9b	(- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

181×	`add-sqr-sqrt`
168×	`times-frac`
166×	`*-un-lft-identity`
87×	`add-cube-cbrt`
86×	`sqrt-prod`
58×	`add-exp-log`
48×	`swap-sqr`
34×	`associate-r` `associate-l` `unswap-sqr`
28×	`distribute-lft-out`
27×	`pow1`
25×	`prod-exp`
24×	`pow-flip`
20×	`add-cbrt-cube`
18×	`unpow-prod-down`
17×	`div-exp`
12×	`div-inv`
10×	`associate-/r/` `pow-prod-up` `sqr-pow`
8×	`rec-exp` `sqrt-pow1` `pow1/2` `sqrt-div` `1-exp` `inv-pow`
7×	`difference-of-squares`
6×	`pow-to-exp` `pow-prod-down` `pow-exp` `pow-sqr` `add-log-exp`
5×	`cbrt-undiv` `associate-/r*` `flip3-+` `cbrt-unprod` `flip-+`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`pow2` `flip3--` `*-commutative` `flip--` `associate-/l/`
1×	`frac-times` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `fma-neg` `diff-log` `div-sub` `prod-diff` `associate-l/` `associate-r/` `un-div-inv`

Counts

4 → 298

Calls

4 calls:

44.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
13.0ms	(* (pow x -1/2) (pow x -1/2))
50.0ms	(/ (- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (pow x -1/2) (/ 1 (sqrt (+ x 1)))))
11.0ms	(- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

series185.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
15.0ms	(* (pow x -1/2) (pow x -1/2))
111.0ms	(/ (- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (pow x -1/2) (/ 1 (sqrt (+ x 1)))))
30.0ms	(- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

simplify1.3s

Counts

310 → 310

Iterations

Iter	Nodes
done	2000
2	2000
1	1214
0	424

prune1.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.6b

regimes26.0ms

Accuracy

100% (0.0b remaining)

Error of 5.6b against oracle of 5.6b and baseline of 29.4b

bsearch60.0ms

Steps

Iters	Range		Point
9	0.1386194397507998	32640636.358721357	8017.181738326081

simplify7.0ms

Iterations

Iter	Nodes
done	40
1	40
0	28

end0.0ms

sample2.4s

Algorithm

intervals

Results

803.0ms	8092×	body	80	nan
581.0ms	1802×	body	640	valid
399.0ms	1169×	body	1280	valid
303.0ms	4126×	body	80	valid
109.0ms	612×	body	320	valid
36.0ms	291×	body	160	valid