Details

sample73.0ms

Algorithm

intervals

Results

26.0ms	43×	body	1280	valid
13.0ms	245×	body	80	nan
10.0ms	44×	body	640	valid
9.0ms	138×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	13
0	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
3.0b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite59.0ms

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:

8.0ms	(sqrt (+ x 1))
16.0ms	(/ 1 (sqrt (+ x 1)))
6.0ms	(/ 1 (sqrt x))
23.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ x 1))
35.0ms	(/ 1 (sqrt (+ x 1)))
41.0ms	(/ 1 (sqrt x))
97.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify2.0s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
3	2576
2	1024
1	407
0	208

prune603.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.2b	(* (sqrt x) (sqrt (+ x 1)))
2.9b	(- (sqrt (+ x 1)) (sqrt x))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
39×	`sqrt-prod`
36×	`*-un-lft-identity`
12×	`difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
10×	`times-frac` `associate-/l*`
9×	`pow1` `distribute-lft-out--`
7×	`associate-r`
6×	`sqrt-div` `associate-l` `add-log-exp`
5×	`distribute-lft-out`
4×	`associate-*r/` `insert-posit16` `unswap-sqr`
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` `associate-/r` `sub-neg` `frac-2neg` `sqrt-unprod` `diff-log` `div-sub` `-commutative` `div-inv`

Counts

4 → 112

Calls

4 calls:

5.0ms	(sqrt (+ x 1))
89.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
29.0ms	(* (sqrt x) (sqrt (+ x 1)))
56.0ms	(- (sqrt (+ x 1)) (sqrt x))

series397.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ x 1))
218.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
77.0ms	(* (sqrt x) (sqrt (+ x 1)))
58.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.7s

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	1291
1	416
0	164

prune546.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
0.2b	(/ (/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.2b	(* (sqrt x) (sqrt (+ x 1)))
2.4b	(- (+ x 1) x)

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

283×	`*-un-lft-identity`
150×	`times-frac`
97×	`distribute-lft-out`
96×	`add-sqr-sqrt`
87×	`sqrt-prod`
48×	`add-cube-cbrt` `associate-/l*`
40×	`distribute-lft-out--`
20×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
9×	`add-log-exp`
8×	`pow1` `associate-/r/`
7×	`cbrt-undiv` `associate-/r` `div-exp` `associate-r*`
6×	`associate-l`
5×	`flip3-+` `flip-+`
4×	`sqrt-div` `associate-*r/` `insert-posit16` `div-inv` `unswap-sqr`
3×	`div-sub` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--`
1×	`sum-log` `sub-neg` `sqrt-unprod` `associate--l+` `*-commutative`

Counts

4 → 226

Calls

4 calls:

115.0ms	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
165.0ms	(/ (/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
33.0ms	(* (sqrt x) (sqrt (+ x 1)))
34.0ms	(- (+ x 1) x)

series423.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
255.0ms	(/ (/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
70.0ms	(* (sqrt x) (sqrt (+ x 1)))
1.0ms	(- (+ x 1) x)

simplify1.8s

Counts

238 → 238

Iterations

Iter	Nodes
done	5002
2	2637
1	745
0	267

prune868.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
78×	`times-frac`
55×	`sqrt-prod`
47×	`add-sqr-sqrt`
45×	`distribute-lft-out`
39×	`add-cube-cbrt`
32×	`add-exp-log`
27×	`associate-/l*`
20×	`add-cbrt-cube`
14×	`div-exp`
9×	`pow1`
8×	`associate-/r/`
7×	`cbrt-undiv` `associate-/r` `associate-r*`
6×	`flip3-+` `associate-l` `flip-+` `add-log-exp`
5×	`prod-exp`
4×	`sqrt-div` `associate-*r/` `insert-posit16` `div-inv` `unswap-sqr`
3×	`rec-exp` `1-exp` `pow-prod-down` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log` `sqrt-unprod` `*-commutative` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 170

Calls

4 calls:

32.0ms	(+ (sqrt (+ x 1)) (sqrt x))
41.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
90.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
20.0ms	(* (sqrt x) (sqrt (+ x 1)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (sqrt (+ x 1)) (sqrt x))
88.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
198.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
59.0ms	(* (sqrt x) (sqrt (+ x 1)))

simplify1.6s

Counts

182 → 182

Iterations

Iter	Nodes
done	5004
2	1996
1	561
0	226

prune564.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	11

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.2s	1824×	body	640	valid
614.0ms	7851×	body	80	nan
503.0ms	1145×	body	1280	valid
410.0ms	4079×	body	80	valid
260.0ms	636×	body	320	valid
121.0ms	316×	body	160	valid