Details

sample66.0ms

Algorithm

intervals

Results

13.0ms	43×	body	1280	valid
12.0ms	245×	body	80	nan
11.0ms	44×	body	640	valid
9.0ms	138×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify12.0ms

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: 17.1b

localize33.0ms

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))))

rewrite68.0ms

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:

4.0ms	(sqrt (+ x 1))
9.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))
45.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ x 1))
34.0ms	(/ 1 (sqrt (+ x 1)))
31.0ms	(/ 1 (sqrt x))
110.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify3.2s

Counts

179 → 179

Iterations

Iter	Nodes
done	5057
4	4762
3	2343
2	988
1	407
0	208

prune622.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.5b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `sqrt-prod`
11×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`pow1`
7×	`associate-r`
6×	`sqrt-div` `associate-l` `add-log-exp`
4×	`associate-*r/` `insert-posit16` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `times-frac` `pow1/2` `pow-prod-down` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--` `distribute-lft-out` `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 → 91

Calls

4 calls:

4.0ms	(sqrt (+ x 1))
33.0ms	(/ (- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1)) (* (sqrt x) (sqrt (+ x 1))))
19.0ms	(* (sqrt x) (sqrt (+ x 1)))
23.0ms	(- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1))

series369.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (+ x 1))
203.0ms	(/ (- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1)) (* (sqrt x) (sqrt (+ x 1))))
59.0ms	(* (sqrt x) (sqrt (+ x 1)))
64.0ms	(- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1))

simplify2.0s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1607
1	435
0	162

prune422.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite327.0ms

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:

103.0ms	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
129.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (* (sqrt x) (sqrt (+ x 1))))
32.0ms	(* (sqrt x) (sqrt (+ x 1)))
54.0ms	(- (+ 1 x) x)

series440.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
241.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (* (sqrt x) (sqrt (+ x 1))))
87.0ms	(* (sqrt x) (sqrt (+ x 1)))
1.0ms	(- (+ 1 x) x)

simplify1.8s

Counts

238 → 238

Iterations

Iter	Nodes
done	5032
2	2347
1	748
0	272

prune855.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
159×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
119×	`add-cube-cbrt`
87×	`sqrt-prod`
29×	`distribute-rgt-out`
21×	`associate-/l*`
20×	`associate-/r/` `distribute-lft-out`
19×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`flip3-+` `flip-+`
11×	`associate-/r*`
10×	`div-inv`
9×	`pow1`
8×	`div-exp`
7×	`associate-l`
6×	`associate-r` `add-log-exp`
4×	`cbrt-undiv` `sqrt-div` `insert-posit16` `unswap-sqr`
3×	`pow-prod-down`
2×	`rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `associate-*l/`
1×	`+-commutative` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 256

Calls

4 calls:

13.0ms	(+ (* (sqrt (+ 1 x)) (sqrt x)) x)
37.0ms	(/ (/ 1 (+ (* (sqrt (+ 1 x)) (sqrt x)) x)) (sqrt (+ x 1)))
32.0ms	(/ 1 (+ (* (sqrt (+ 1 x)) (sqrt x)) x))
16.0ms	(* (sqrt (+ 1 x)) (sqrt x))

series419.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ (* (sqrt (+ 1 x)) (sqrt x)) x)
153.0ms	(/ (/ 1 (+ (* (sqrt (+ 1 x)) (sqrt x)) x)) (sqrt (+ x 1)))
105.0ms	(/ 1 (+ (* (sqrt (+ 1 x)) (sqrt x)) x))
89.0ms	(* (sqrt (+ 1 x)) (sqrt x))

simplify1.8s

Counts

268 → 268

Iterations

Iter	Nodes
done	5001
2	2306
1	880
0	370

prune761.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	11

end0.0ms

sample1.7s

Algorithm

intervals

Results

670.0ms	1824×	body	640	valid
376.0ms	7851×	body	80	nan
246.0ms	1145×	body	1280	valid
194.0ms	4079×	body	80	valid
73.0ms	636×	body	320	valid
23.0ms	316×	body	160	valid