Details

sample111.0ms

Algorithm

intervals

Results

27.0ms	259×	body	80	nan
26.0ms	59×	body	640	valid
19.0ms	36×	body	1280	valid
15.0ms	137×	body	80	valid
6.0ms	17×	body	320	valid
2.0ms	7×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	13
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
2.6b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
97×	`times-frac`
93×	`*-un-lft-identity`
60×	`sqrt-prod`
40×	`add-cube-cbrt`
25×	`difference-of-squares`
13×	`associate-/r*` `distribute-lft-out--`
11×	`add-exp-log`
7×	`pow1` `add-cbrt-cube` `distribute-lft-out`
6×	`div-inv` `pow-flip` `associate-/l*`
5×	`add-log-exp`
4×	`div-exp`
3×	`insert-posit16`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `1-exp` `associate-/r/` `inv-pow`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `frac-sub` `flip-+` `flip--`

Counts

3 → 150

Calls

3 calls:

16.0ms	(/ 1 (sqrt (+ x 1)))
9.0ms	(/ 1 (sqrt x))
61.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series190.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ 1 (sqrt (+ x 1)))
41.0ms	(/ 1 (sqrt x))
104.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify1.1s

Counts

159 → 159

Iterations

Iter	Nodes
done	2006
3	2006
2	929
1	383
0	196

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.1b

localize35.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
11.0b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`times-frac`
22×	`sqrt-prod`
18×	`add-cube-cbrt`
15×	`difference-of-squares`
7×	`associate-/r*`
6×	`add-exp-log`
5×	`unpow-prod-down` `sqr-pow`
4×	`pow1` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
3×	`pow-flip` `associate-/l*`
2×	`sqrt-div` `div-exp` `associate-/r/` `insert-posit16` `div-inv` `distribute-lft-out--`
1×	`cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `1-exp` `flip-+` `flip--` `inv-pow`

Counts

2 → 82

Calls

2 calls:

17.0ms	(/ 1 (sqrt (+ x 1)))
43.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series126.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ 1 (sqrt (+ x 1)))
72.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify1.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	2000
4	2000
3	1950
2	799
1	321
0	156

prune834.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.1b

localize41.0ms

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))
1.0b	(/ (- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (pow x -1/2) (/ 1 (sqrt (+ x 1)))))
9.8b	(- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

rewrite156.0ms

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×	`insert-posit16` `associate-/l*`
2×	`pow2` `flip3--` `*-commutative` `flip--` `associate-/l/`
1×	`frac-times` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `associate-l/` `associate-r/` `un-div-inv`

Counts

4 → 288

Calls

4 calls:

51.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
13.0ms	(* (pow x -1/2) (pow x -1/2))
65.0ms	(/ (- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (pow x -1/2) (/ 1 (sqrt (+ x 1)))))
16.0ms	(- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
16.0ms	(* (pow x -1/2) (pow x -1/2))
148.0ms	(/ (- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (pow x -1/2) (/ 1 (sqrt (+ x 1)))))
49.0ms	(- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

simplify1.5s

Counts

300 → 300

Iterations

Iter	Nodes
done	2003
2	2003
1	1202
0	413

prune3.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 5.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
1.5b	(/ (- (/ 1 x) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (pow x -1/2) (/ 1 (sqrt (+ x 1)))))
16.9b	(- (/ 1 x) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

213×	`times-frac`
207×	`add-sqr-sqrt`
197×	`*-un-lft-identity`
102×	`sqrt-prod`
97×	`add-cube-cbrt`
50×	`add-exp-log`
41×	`swap-sqr`
36×	`distribute-lft-out`
29×	`pow1`
27×	`associate-r` `associate-l` `pow-flip`
25×	`unswap-sqr`
21×	`difference-of-squares`
20×	`add-cbrt-cube`
19×	`div-exp`
16×	`prod-exp`
15×	`div-inv`
12×	`associate-/r*` `associate-/r/`
10×	`sqrt-div`
9×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-up` `associate-/l*` `inv-pow`
8×	`frac-sub`
6×	`cbrt-undiv` `flip3-+` `flip-+` `add-log-exp` `associate-/l/`
5×	`pow-prod-down` `pow-sqr`
4×	`cbrt-unprod` `insert-posit16`
3×	`frac-times` `associate-l/` `associate-r/` `un-div-inv`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `div-sub` `*-commutative`

Counts

4 → 309

Calls

4 calls:

9.0ms	(/ 1 (sqrt (+ x 1)))
48.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
66.0ms	(/ (- (/ 1 x) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (pow x -1/2) (/ 1 (sqrt (+ x 1)))))
18.0ms	(- (/ 1 x) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

series201.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (sqrt (+ x 1)))
14.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
114.0ms	(/ (- (/ 1 x) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (pow x -1/2) (/ 1 (sqrt (+ x 1)))))
39.0ms	(- (/ 1 x) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

simplify1.2s

Counts

321 → 321

Iterations

Iter	Nodes
done	2002
2	2002
1	1200
0	414

prune3.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 5.7b

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 5.5b against oracle of 5.5b and baseline of 25.8b

bsearch62.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	318690.85562629136	8764.773044208743

simplify4.0ms

Iterations

Iter	Nodes
done	30
1	30
0	24

end0.0ms

sample2.4s

Algorithm

intervals

Results

725.0ms	8060×	body	80	nan
562.0ms	1830×	body	640	valid
445.0ms	1147×	body	1280	valid
329.0ms	4063×	body	80	valid
137.0ms	649×	body	320	valid
36.0ms	311×	body	160	valid