Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	276×	body	80	nan
4.0ms	54×	body	1280	valid
3.0ms	52×	body	640	valid
3.0ms	128×	body	80	valid
1.0ms	12×	body	320	valid
0.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

4.0ms	(sqrt (+ x 1.0))
22.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series107.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(sqrt (+ x 1.0))
72.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.1s

Counts

41 → 41

Iterations

Useful iterations: 4 (1.0s)

Iter	Nodes	Cost
0	84	488
1	183	440
2	452	410
3	1180	402
4	3522	389
done	5000	389

prune85.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
17.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
27.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series245.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (+ x 1.0))
69.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
146.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.8s

Counts

80 → 80

Iterations

Useful iterations: 3 (572.0ms)

Iter	Nodes	Cost
0	152	1125
1	343	1034
2	919	939
3	3047	923
done	5000	923

prune170.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

26.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
26.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
126.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series784.0ms

Counts

4 → 12

Calls

4 calls:

338.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
137.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
138.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
170.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify921.0ms

Counts

262 → 262

Iterations

Useful iterations: done (912.0ms)

Iter	Nodes	Cost
0	311	6170
1	647	4458
2	2098	4132
done	5001	4126

prune566.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b	(/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(pow (/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1 2))
0.3b	(* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity`
31×	`add-exp-log`
28×	`sqrt-prod` `distribute-lft-out`
19×	`flip3-+` `flip-+`
18×	`add-sqr-sqrt` `add-cbrt-cube`
16×	`add-cube-cbrt` `associate-/r/`
13×	`unpow-prod-down` `pow-unpow`
12×	`pow1` `frac-times`
11×	`times-frac`
10×	`swap-sqr`
9×	`prod-exp`
8×	`div-exp`
6×	`associate-r/` `associate-r` `associate-l` `associate-l/` `add-log-exp`
5×	`pow-exp` `cbrt-unprod`
4×	`cbrt-undiv`
3×	`div-inv`
1×	`+-commutative` `pow2` `distribute-rgt-in` `pow-to-exp` `pow-pow` `frac-2neg` `distribute-lft-in` `pow-plus` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `pow-sqr` `-commutative` `pow-prod-up` `associate-/l*` `unswap-sqr` `sqr-pow`

Counts

4 → 132

Calls

4 calls:

18.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
29.0ms	(/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x))))
37.0ms	(pow (/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1 2))
104.0ms	(* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))

series932.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
190.0ms	(/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x))))
569.0ms	(pow (/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1 2))
105.0ms	(* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.3s

Counts

144 → 144

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	283	3922
1	816	3259
2	2915	2806
done	5000	2800

prune340.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	22	29
done	22	29

end0.0ms

sample674.0ms

Algorithm

intervals

Results

149.0ms	1723×	body	1280	valid
142.0ms	8134×	body	80	nan
85.0ms	1260×	body	640	valid
76.0ms	4068×	body	80	valid
31.0ms	621×	body	320	valid
11.0ms	328×	body	160	valid