Details

sample98.0ms

Algorithm

intervals

Results

22.0ms	53×	body	640	valid
20.0ms	36×	body	1280	valid
20.0ms	229×	body	80	nan
14.0ms	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

localize22.0ms

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))))

rewrite102.0ms

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))
18.0ms	(/ 1 (sqrt (+ x 1)))
10.0ms	(/ 1 (sqrt x))
60.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ x 1))
55.0ms	(/ 1 (sqrt (+ x 1)))
33.0ms	(/ 1 (sqrt x))
84.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify3.5s

Counts

179 → 179

Iterations

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

prune664.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.3b

localize23.0ms

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)))
2.7b	(- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1))

rewrite110.0ms

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:

10.0ms	(sqrt (+ x 1))
57.0ms	(/ (- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1)) (* (sqrt x) (sqrt (+ x 1))))
18.0ms	(* (sqrt x) (sqrt (+ x 1)))
23.0ms	(- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1))

series414.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ x 1))
222.0ms	(/ (- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1)) (* (sqrt x) (sqrt (+ x 1))))
60.0ms	(* (sqrt x) (sqrt (+ x 1)))
92.0ms	(- (* 1 (sqrt (+ x 1))) (* (sqrt x) 1))

simplify2.2s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1607
1	435
0	162

prune515.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.5b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite279.0ms

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:

69.0ms	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
155.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (* (sqrt x) (sqrt (+ x 1))))
22.0ms	(* (sqrt x) (sqrt (+ x 1)))
24.0ms	(- (+ 1 x) x)

series459.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))))
269.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (* (sqrt x) (sqrt (+ x 1))))
93.0ms	(* (sqrt x) (sqrt (+ x 1)))
2.0ms	(- (+ 1 x) x)

simplify1.9s

Counts

238 → 238

Iterations

Iter	Nodes
done	5032
2	2347
1	748
0	272

prune722.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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

rewrite440.0ms

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:

15.0ms	(+ (* (sqrt (+ 1 x)) (sqrt x)) x)
348.0ms	(/ 1 (+ (* (sqrt (+ 1 x)) (sqrt x)) x))
47.0ms	(/ (/ 1 (+ (* (sqrt (+ 1 x)) (sqrt x)) x)) (sqrt (+ x 1)))
22.0ms	(* (sqrt (+ 1 x)) (sqrt x))

series374.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(+ (* (sqrt (+ 1 x)) (sqrt x)) x)
79.0ms	(/ 1 (+ (* (sqrt (+ 1 x)) (sqrt x)) x))
168.0ms	(/ (/ 1 (+ (* (sqrt (+ 1 x)) (sqrt x)) x)) (sqrt (+ x 1)))
65.0ms	(* (sqrt (+ 1 x)) (sqrt x))

simplify1.7s

Counts

268 → 268

Iterations

Iter	Nodes
done	5001
2	2332
1	881
0	370

prune936.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes70.0ms

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	17
1	17
0	12

end0.0ms

sample2.7s

Algorithm

intervals

Results

864.0ms	7961×	body	80	nan
587.0ms	1799×	body	640	valid
473.0ms	1102×	body	1280	valid
391.0ms	4171×	body	80	valid
132.0ms	604×	body	320	valid
69.0ms	324×	body	160	valid