Details

sample98.0ms

Algorithm

intervals

Results

23.0ms	59×	body	640	valid
22.0ms	272×	body	80	nan
17.0ms	41×	body	1280	valid
12.0ms	123×	body	80	valid
5.0ms	19×	body	320	valid
3.0ms	14×	body	160	valid

simplify26.0ms

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: 20.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
4.8b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite70.0ms

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))
9.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))
44.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series200.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ x 1))
35.0ms	(/ 1 (sqrt (+ x 1)))
49.0ms	(/ 1 (sqrt x))
83.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify1.5s

Counts

179 → 179

Iterations

Iter	Nodes
done	5001
2	1885
1	436
0	208

prune583.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 19.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.3b	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
0.4b	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
4.8b	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

426×	`times-frac`
387×	`*-un-lft-identity`
340×	`add-sqr-sqrt`
208×	`sqrt-prod`
176×	`add-cube-cbrt`
98×	`distribute-lft-out`
86×	`add-exp-log`
71×	`swap-sqr`
50×	`pow1` `unswap-sqr`
49×	`associate-r` `associate-l`
48×	`pow-flip`
33×	`div-exp` `div-inv`
32×	`prod-exp` `frac-sub`
30×	`add-cbrt-cube`
18×	`frac-times` `associate-l/` `associate-r/` `un-div-inv` `pow-prod-up` `difference-of-squares` `associate-/l/`
16×	`rec-exp` `associate-/r*` `sqrt-pow1` `pow1/2` `1-exp` `inv-pow`
11×	`associate-/r/`
10×	`pow-prod-down` `pow-sqr`
9×	`cbrt-undiv`
8×	`sqrt-div` `cbrt-unprod`
6×	`add-log-exp`
5×	`flip3-+` `flip-+`
4×	`insert-posit16` `associate-/l*`
2×	`pow2` `pow-plus` `flip3--` `*-commutative` `flip--`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `frac-add`

Counts

4 → 476

Calls

4 calls:

105.0ms	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
73.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
38.0ms	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
36.0ms	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
24.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
25.0ms	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
67.0ms	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

simplify1.9s

Counts

488 → 488

Iterations

Iter	Nodes
done	5000
1	1830
0	513

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 5.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
0.2b	(/ (/ (- (+ 1 x) x) (* (+ 1 x) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
4.4b	(- (+ 1 x) x)

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

583×	`*-un-lft-identity`
567×	`times-frac`
230×	`distribute-lft-out`
196×	`add-sqr-sqrt`
184×	`sqrt-prod`
160×	`add-cube-cbrt`
72×	`div-inv`
39×	`associate-/r/`
36×	`distribute-lft-out--`
34×	`associate-*l/`
29×	`associate-/r*`
21×	`add-exp-log`
19×	`flip3-+` `flip-+`
18×	`associate-/l*` `difference-of-squares`
17×	`add-cbrt-cube`
9×	`div-exp` `add-log-exp`
8×	`pow1`
7×	`cbrt-undiv`
6×	`pow-flip`
4×	`insert-posit16`
3×	`clear-num` `frac-2neg`
2×	`rec-exp` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `1-exp` `div-sub` `inv-pow`
1×	`sum-log` `sub-neg` `flip3--` `frac-add` `prod-exp` `associate--l+` `cbrt-unprod` `flip--` `associate-/l/`

Counts

4 → 358

Calls

4 calls:

9.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))
85.0ms	(/ (/ (- (+ 1 x) x) (* (+ 1 x) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
24.0ms	(- (+ 1 x) x)

series278.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 1 (sqrt (+ x 1)))
40.0ms	(/ 1 (sqrt x))
194.0ms	(/ (/ (- (+ 1 x) x) (* (+ 1 x) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
1.0ms	(- (+ 1 x) x)

simplify1.3s

Counts

370 → 370

Iterations

Iter	Nodes
done	5001
1	1211
0	429

prune866.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sqrt (+ 1 x)))
0.1b	(* (/ 1 (+ 1 x)) (/ (/ (+ 1 0) x) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ 1 x))))))
0.2b	(/ 1 (sqrt x))
0.4b	(/ (/ (+ 1 0) x) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ 1 x)))))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

1579×	`*-un-lft-identity`
1568×	`times-frac`
634×	`distribute-lft-out`
569×	`add-sqr-sqrt`
539×	`add-cube-cbrt`
424×	`sqrt-prod`
263×	`associate-r`
170×	`div-inv`
56×	`add-exp-log`
34×	`add-cbrt-cube`
29×	`associate-/r*`
25×	`div-exp`
22×	`associate-/l*`
18×	`associate-l`
14×	`cbrt-undiv`
12×	`prod-exp`
10×	`pow1` `associate-/r/`
9×	`unswap-sqr`
6×	`cbrt-unprod` `pow-flip`
5×	`rec-exp` `1-exp`
4×	`flip3-+` `flip-+` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `frac-add` `inv-pow`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 726

Calls

4 calls:

15.0ms	(/ 1 (sqrt (+ 1 x)))
122.0ms	(* (/ 1 (+ 1 x)) (/ (/ (+ 1 0) x) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ 1 x))))))
9.0ms	(/ 1 (sqrt x))
84.0ms	(/ (/ (+ 1 0) x) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ 1 x)))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 1 (sqrt (+ 1 x)))
180.0ms	(* (/ 1 (+ 1 x)) (/ (/ (+ 1 0) x) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ 1 x))))))
47.0ms	(/ 1 (sqrt x))
171.0ms	(/ (/ (+ 1 0) x) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ 1 x)))))

simplify2.6s

Counts

738 → 738

Iterations

Iter	Nodes
done	5001
1	2256
0	622

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes33.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample2.5s

Algorithm

intervals

Results

563.0ms	4040×	body	80	valid
537.0ms	1852×	body	640	valid
515.0ms	8083×	body	80	nan
482.0ms	1185×	body	1280	valid
178.0ms	605×	body	320	valid
39.0ms	318×	body	160	valid