Details

sample105.0ms

Algorithm

intervals

Results

24.0ms	53×	body	640	valid
22.0ms	229×	body	80	nan
21.0ms	36×	body	1280	valid
17.0ms	143×	body	80	valid
4.0ms	13×	body	320	valid
2.0ms	11×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	13
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
2.7b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 322

Calls

4 calls:

13.0ms	(sqrt (+ x 1))
25.0ms	(/ 1 (sqrt (+ x 1)))
13.0ms	(/ 1 (sqrt x))
141.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series218.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ x 1))
36.0ms	(/ 1 (sqrt (+ x 1)))
52.0ms	(/ 1 (sqrt x))
93.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify2.2s

Counts

334 → 334

Iterations

Iter	Nodes
done	5002
2	2902
1	1478
0	512

prune722.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 18.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
0.2b	(* (sqrt (+ x 1)) (sqrt x))
2.7b	(- (sqrt (+ x 1)) (sqrt x))

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

376×	`add-sqr-sqrt`
328×	`sqrt-prod`
281×	`*-un-lft-identity`
220×	`times-frac`
96×	`difference-of-squares`
87×	`add-cube-cbrt`
84×	`associate-l`
72×	`associate-r` `distribute-lft-out--`
48×	`unswap-sqr`
37×	`distribute-lft-out`
22×	`associate-/r*`
12×	`*-commutative`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/l*`
9×	`pow1`
6×	`sqrt-div` `add-log-exp`
4×	`associate-*l/` `insert-posit16`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-unprod` `diff-log` `div-sub` `div-inv`

Counts

4 → 343

Calls

4 calls:

13.0ms	(sqrt (+ x 1))
142.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
40.0ms	(* (sqrt (+ x 1)) (sqrt x))
53.0ms	(- (sqrt (+ x 1)) (sqrt x))

series377.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt (+ x 1))
226.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
59.0ms	(* (sqrt (+ x 1)) (sqrt x))
67.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify2.4s

Counts

355 → 355

Iterations

Iter	Nodes
done	5002
2	2386
1	794
0	285

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 17.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt (+ x 1)) (sqrt x)))
0.2b	(* (sqrt (+ x 1)) (sqrt x))
1.7b	(- (+ 1 x) x)

rewrite646.0ms

Algorithm

rewrite-expression-head

Rules

2383×	`*-un-lft-identity`
1788×	`times-frac`
1184×	`add-sqr-sqrt`
1068×	`sqrt-prod`
775×	`distribute-lft-out`
538×	`add-cube-cbrt`
308×	`associate-l`
294×	`distribute-lft-out--`
264×	`associate-r`
176×	`unswap-sqr`
147×	`difference-of-squares`
54×	`associate-/l*`
50×	`associate-/r/`
44×	`*-commutative`
34×	`associate-/r*`
26×	`flip3-+` `flip-+`
25×	`div-inv`
21×	`associate-/l/`
20×	`add-cbrt-cube` `add-exp-log`
9×	`add-log-exp`
8×	`pow1`
7×	`cbrt-undiv` `div-exp`
4×	`sqrt-div` `associate-*l/` `insert-posit16`
3×	`clear-num` `frac-2neg` `flip3--` `div-sub` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sqrt-pow1` `pow1/2` `diff-log` `associate--l+`
1×	`+-commutative` `sum-log` `sub-neg` `sqrt-unprod`

Counts

4 → 1146

Calls

4 calls:

168.0ms	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
261.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt (+ x 1)) (sqrt x)))
35.0ms	(* (sqrt (+ x 1)) (sqrt x))
45.0ms	(- (+ 1 x) x)

series502.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
316.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt (+ x 1)) (sqrt x)))
76.0ms	(* (sqrt (+ x 1)) (sqrt x))
2.0ms	(- (+ 1 x) x)

simplify2.5s

Counts

1158 → 1158

Iterations

Iter	Nodes
done	5002
1	2337
0	776

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.2b	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt (+ x 1)) (sqrt x)))
0.2b	(* (sqrt (+ x 1)) (sqrt x))

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

960×	`times-frac`
949×	`*-un-lft-identity`
586×	`add-sqr-sqrt` `sqrt-prod`
377×	`add-cube-cbrt`
323×	`distribute-lft-out`
182×	`associate-l`
156×	`associate-r`
104×	`unswap-sqr`
50×	`associate-/r/`
34×	`associate-/r*`
32×	`add-exp-log`
30×	`associate-/l*`
27×	`flip3-+` `flip-+`
26×	`*-commutative`
25×	`div-inv`
20×	`add-cbrt-cube`
14×	`div-exp`
12×	`associate-/l/`
10×	`pow1`
7×	`cbrt-undiv`
6×	`sqrt-div`
5×	`prod-exp`
4×	`associate-*l/` `insert-posit16` `add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `cbrt-unprod`
1×	`rem-sqrt-square` `sqrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 708

Calls

4 calls:

7.0ms	(sqrt (+ x 1))
41.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
227.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt (+ x 1)) (sqrt x)))
50.0ms	(* (sqrt (+ x 1)) (sqrt x))

series433.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ x 1))
91.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
238.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt (+ x 1)) (sqrt x)))
68.0ms	(* (sqrt (+ x 1)) (sqrt x))

simplify3.8s

Counts

720 → 720

Iterations

Iter	Nodes
done	5016
2	4987
1	1841
0	619

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes70.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	23
1	23
0	16

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.2s	7961×	body	80	nan
687.0ms	1799×	body	640	valid
533.0ms	1102×	body	1280	valid
390.0ms	4171×	body	80	valid
147.0ms	604×	body	320	valid
104.0ms	324×	body	160	valid