Details

sample95.0ms

Algorithm

intervals

Results

17.0ms	272×	body	80	nan
17.0ms	41×	body	1280	valid
16.0ms	59×	body	640	valid
10.0ms	123×	body	80	valid
4.0ms	19×	body	320	valid
2.0ms	14×	body	160	valid

simplify41.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.0b

localize90.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
4.8b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
69×	`times-frac`
50×	`sqrt-prod`
42×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div` `insert-posit16` `div-inv`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 137

Calls

4 calls:

29.0ms	(sqrt (+ x 1.0))
36.0ms	(/ 1.0 (sqrt (+ x 1.0)))
12.0ms	(/ 1.0 (sqrt x))
137.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ x 1.0))
96.0ms	(/ 1.0 (sqrt (+ x 1.0)))
69.0ms	(/ 1.0 (sqrt x))
188.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify6.8s

Counts

149 → 149

Iterations

Iter	Nodes
done	5019
3	3556
2	1183
1	466
0	220

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.3b

localize179.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.3b	(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
0.4b	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
4.8b	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite681.0ms

Algorithm

rewrite-expression-head

Rules

362×	`times-frac`
331×	`*-un-lft-identity`
258×	`add-sqr-sqrt`
180×	`sqrt-prod`
174×	`add-cube-cbrt`
88×	`distribute-lft-out`
67×	`swap-sqr`
49×	`associate-r` `associate-l`
30×	`add-cbrt-cube` `add-exp-log`
19×	`div-inv`
18×	`pow1` `frac-sub` `unswap-sqr`
16×	`difference-of-squares`
14×	`frac-times` `associate-/r` `associate-l/` `associate-*r/`
11×	`associate-/r/` `associate-/l/`
9×	`cbrt-undiv` `div-exp`
8×	`sqrt-div` `prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`flip3-+` `flip-+`
4×	`insert-posit16` `associate-/l*`
2×	`pow2` `pow-plus` `flip3--` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `frac-add`

Counts

4 → 358

Calls

4 calls:

362.0ms	(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
151.0ms	(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
69.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
39.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series640.0ms

Counts

4 → 12

Calls

4 calls:

479.0ms	(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
42.0ms	(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
38.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
80.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify3.8s

Counts

370 → 370

Iterations

Iter	Nodes
done	5000
1	1746
0	523

prune2.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize220.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.5b	(* (sqrt x) (sqrt x))
0.5b	(* (sqrt x) (sqrt x))
4.4b	(- (* (* 1.0 1.0) (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))) (* (* (sqrt x) (sqrt x)) (* 1.0 1.0)))

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
62×	`sqrt-prod`
49×	`pow1`
42×	`*-un-lft-identity`
28×	`add-cube-cbrt`
27×	`swap-sqr`
24×	`sqrt-pow1` `pow1/2`
19×	`associate-r` `associate-l`
15×	`pow-prod-up`
12×	`sqrt-div` `unswap-sqr`
10×	`add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `pow-sqr`
6×	`flip3-+` `flip-+` `distribute-lft-out` `add-log-exp`
4×	`frac-times` `insert-posit16`
3×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`
2×	`associate-l/` `associate-r/`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 176

Calls

4 calls:

91.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
41.0ms	(* (sqrt x) (sqrt x))
31.0ms	(* (sqrt x) (sqrt x))
202.0ms	(- (* (* 1.0 1.0) (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))) (* (* (sqrt x) (sqrt x)) (* 1.0 1.0)))

series99.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
21.0ms	(* (sqrt x) (sqrt x))
23.0ms	(* (sqrt x) (sqrt x))
26.0ms	(- (* (* 1.0 1.0) (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))) (* (* (sqrt x) (sqrt x)) (* 1.0 1.0)))

simplify2.4s

Counts

188 → 188

Iterations

Iter	Nodes
done	5000
2	1136
1	366
0	150

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.6b

localize132.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.5b	(* (sqrt x) (sqrt x))
0.7b	(/ 1.0 (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))))
4.9b	(/ (/ 1.0 (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite736.0ms

Algorithm

rewrite-expression-head

Rules

546×	`*-un-lft-identity` `times-frac`
236×	`sqrt-prod`
230×	`distribute-lft-out`
204×	`sqrt-div`
188×	`add-sqr-sqrt`
164×	`add-cube-cbrt`
162×	`associate-*r/`
131×	`associate-/r/`
103×	`flip3-+` `flip-+`
68×	`frac-times`
51×	`add-cbrt-cube` `add-exp-log`
49×	`div-inv`
34×	`pow1` `associate-*l/`
19×	`swap-sqr`
18×	`prod-exp` `cbrt-unprod` `associate-/l*`
16×	`cbrt-undiv` `sqrt-pow1` `pow1/2` `div-exp`
15×	`associate-/r*`
13×	`associate-r` `associate-l`
10×	`pow-prod-up`
8×	`unswap-sqr`
6×	`pow-prod-down` `pow-sqr`
4×	`insert-posit16` `add-log-exp`
2×	`pow2` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `*-commutative`
1×	`frac-add` `associate-/l/`

Counts

4 → 415

Calls

4 calls:

79.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
28.0ms	(* (sqrt x) (sqrt x))
159.0ms	(/ 1.0 (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))))
377.0ms	(/ (/ 1.0 (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

series670.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
19.0ms	(* (sqrt x) (sqrt x))
59.0ms	(/ 1.0 (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))))
568.0ms	(/ (/ 1.0 (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

simplify3.1s

Counts

427 → 427

Iterations

Iter	Nodes
done	5000
1	1682
0	568

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes149.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample2.2s

Algorithm

intervals

Results

445.0ms	8083×	body	80	nan
425.0ms	1852×	body	640	valid
372.0ms	4040×	body	80	valid
363.0ms	605×	body	320	valid
327.0ms	1185×	body	1280	valid
32.0ms	318×	body	160	valid