Details

sample118.0ms

Algorithm

intervals

Results

30.0ms	29×	body	1280	valid
29.0ms	71×	body	640	valid
23.0ms	271×	body	80	nan
15.0ms	132×	body	80	valid
4.0ms	14×	body	320	valid
2.0ms	10×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	15
2	15
1	11
0	8

prune6.0ms

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))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
97×	`*-un-lft-identity` `times-frac`
64×	`sqrt-prod`
42×	`add-cube-cbrt`
25×	`difference-of-squares`
13×	`associate-/r*` `distribute-lft-out--`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube` `distribute-lft-out`
6×	`div-inv` `pow-flip` `associate-/l*` `add-log-exp`
4×	`sqrt-div` `div-exp` `insert-posit16`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `associate-/r/` `flip-+` `inv-pow`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 167

Calls

4 calls:

5.0ms	(sqrt (+ x 1))
14.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))
26.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series233.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ x 1))
48.0ms	(/ 1 (sqrt (+ x 1)))
46.0ms	(/ 1 (sqrt x))
100.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify7.3s

Counts

179 → 179

Iterations

Iter	Nodes
3	2042
2	940
1	393
0	208

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (sqrt x))
0.3b	(* (sqrt (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (sqrt (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))
2.5b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
2.5b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

831×	`add-sqr-sqrt`
666×	`sqrt-prod`
598×	`times-frac`
515×	`*-un-lft-identity`
262×	`difference-of-squares`
128×	`swap-sqr`
122×	`distribute-lft-out--`
71×	`add-cube-cbrt`
57×	`div-inv`
44×	`associate-r` `associate-l`
24×	`sqrt-div` `distribute-lft-out`
21×	`pow1`
10×	`flip3--` `add-exp-log` `frac-sub` `flip--`
9×	`frac-times` `sqrt-pow1` `pow1/2`
8×	`add-cbrt-cube` `add-log-exp`
6×	`associate-/r*`
5×	`pow-prod-up`
4×	`insert-posit16` `unswap-sqr`
3×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-flip` `associate-/l*`
2×	`sub-neg` `diff-log` `div-exp`
1×	`pow2` `cbrt-undiv` `rec-exp` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `1-exp` `prod-exp` `*-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 411

Calls

4 calls:

5.0ms	(/ 1 (sqrt x))
150.0ms	(* (sqrt (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (sqrt (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))
36.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
26.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1 (sqrt x))
110.0ms	(* (sqrt (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (sqrt (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))
111.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
118.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify6.1s

Counts

423 → 423

Iterations

Iter	Nodes
3	2453
2	1116
1	519
0	294

prune3.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 19.1b

localize17.0ms

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))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
33×	`times-frac`
26×	`sqrt-prod`
20×	`add-cube-cbrt`
15×	`difference-of-squares`
7×	`associate-/r*` `add-exp-log`
6×	`pow1`
5×	`unpow-prod-down` `add-cbrt-cube` `distribute-lft-out` `add-log-exp` `sqr-pow`
4×	`sqrt-div`
3×	`insert-posit16` `pow-flip` `associate-/l*`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `associate-/r/` `flip-+` `div-inv` `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 → 99

Calls

3 calls:

4.0ms	(sqrt (+ x 1))
9.0ms	(/ 1 (sqrt (+ x 1)))
18.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series120.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(sqrt (+ x 1))
29.0ms	(/ 1 (sqrt (+ x 1)))
65.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify2.6s

Counts

108 → 108

Iterations

Iter	Nodes
4	4796
3	1798
2	804
1	351
0	173

prune624.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 19.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ 1 (sqrt x))
8.5b	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 76

Calls

2 calls:

5.0ms	(/ 1 (sqrt x))
29.0ms	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))

series94.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ 1 (sqrt x))
67.0ms	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))

simplify797.0ms

Counts

82 → 82

Iterations

Iter	Nodes
3	2204
2	874
1	356
0	168

prune432.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.1b

regimes61.0ms

Accuracy

87.7% (0.4b remaining)

Error of 19.6b against oracle of 19.2b and baseline of 22.4b

bsearch43.0ms

Steps

Iters	Range		Point
5	1.54233224591644e+116	4.056420738895485e+116	2.6546736668899873e+116

simplify5.0ms

Iterations

Iter	Nodes
2	30
1	30
0	26

end0.0ms

sample2.3s

Algorithm

intervals

Results

676.0ms	1161×	body	1280	valid
508.0ms	8041×	body	80	nan
502.0ms	1848×	body	640	valid
286.0ms	4103×	body	80	valid
119.0ms	596×	body	320	valid
35.0ms	292×	body	160	valid