Details

sample79.0ms

Algorithm

intervals

Results

19.0ms	298×	body	80	nan
15.0ms	37×	body	1280	valid
14.0ms	51×	body	640	valid
13.0ms	135×	body	80	valid
5.0ms	25×	body	320	valid
1.0ms	8×	body	160	valid

simplify6.0ms

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: 18.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
2.6b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite84.0ms

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:

9.0ms	(sqrt (+ x 1))
19.0ms	(/ 1 (sqrt (+ x 1)))
8.0ms	(/ 1 (sqrt x))
43.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series173.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (+ x 1))
36.0ms	(/ 1 (sqrt (+ x 1)))
30.0ms	(/ 1 (sqrt x))
84.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify6.8s

Counts

179 → 179

Iterations

Iter	Nodes
3	2042
2	940
1	393
0	208

prune811.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
11.5b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite46.0ms

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:

13.0ms	(sqrt (+ x 1))
11.0ms	(/ 1 (sqrt (+ x 1)))
19.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series135.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(sqrt (+ x 1))
40.0ms	(/ 1 (sqrt (+ x 1)))
71.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify3.4s

Counts

108 → 108

Iterations

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

prune515.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1) -1/2)
0.2b	(/ 1 (sqrt x))
11.5b	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 95

Calls

3 calls:

10.0ms	(pow (+ x 1) -1/2)
12.0ms	(/ 1 (sqrt x))
41.0ms	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))

series148.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(pow (+ x 1) -1/2)
32.0ms	(/ 1 (sqrt x))
81.0ms	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))

simplify1.7s

Counts

104 → 104

Iterations

Iter	Nodes
3	2489
2	1022
1	415
0	195

prune551.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (- (/ 1 (sqrt x)) (pow (+ x 1) -1/2)))
11.5b	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))
11.5b	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))
11.5b	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

129×	`add-sqr-sqrt`
60×	`difference-of-squares`
48×	`times-frac`
41×	`*-un-lft-identity`
24×	`sqrt-prod`
20×	`cbrt-prod` `unpow-prod-down` `sqr-pow`
10×	`add-log-exp`
8×	`distribute-lft-out--`
5×	`add-cube-cbrt`
4×	`pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `div-inv` `flip--`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 121

Calls

4 calls:

20.0ms	(cbrt (- (/ 1 (sqrt x)) (pow (+ x 1) -1/2)))
29.0ms	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))
27.0ms	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))
31.0ms	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))

series434.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt (- (/ 1 (sqrt x)) (pow (+ x 1) -1/2)))
79.0ms	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))
90.0ms	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))
87.0ms	(- (/ 1 (sqrt x)) (pow (+ x 1) -1/2))

simplify3.0s

Counts

133 → 133

Iterations

Iter	Nodes
3	5097
2	1482
1	521
0	215

prune929.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.1b

regimes77.0ms

Accuracy

94.4% (0.3b remaining)

Error of 19.3b against oracle of 19.0b and baseline of 24.7b

bsearch62.0ms

Steps

Iters	Range		Point
5	1.0317583027926416e+141	2.0932662470405204e+141	1.189590584318109e+141

simplify6.0ms

Iterations

Iter	Nodes
2	22
1	22
0	20

end0.0ms

sample2.7s

Algorithm

intervals

Results

803.0ms	1117×	body	1280	valid
641.0ms	1831×	body	640	valid
598.0ms	8131×	body	80	nan
317.0ms	4141×	body	80	valid
132.0ms	607×	body	320	valid
46.0ms	304×	body	160	valid