Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	62×	body	640	valid
6.0ms	238×	body	80	nan
6.0ms	39×	body	1280	valid
4.0ms	123×	body	80	valid
2.0ms	25×	body	320	valid
0.0ms	7×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.7b

localize28.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
2.7b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
875×	`*-un-lft-identity`
742×	`add-sqr-sqrt`
712×	`add-cube-cbrt`
594×	`prod-diff`
562×	`sqrt-prod`
73×	`distribute-lft-out`
54×	`div-inv`
46×	`sqrt-div` `associate-/r/`
23×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

3 → 739

Calls

3 calls:

17.0ms	(/ 1.0 (sqrt (+ x 1.0)))
9.0ms	(/ 1.0 (sqrt x))
117.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series386.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(/ 1.0 (sqrt (+ x 1.0)))
52.0ms	(/ 1.0 (sqrt x))
199.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.6s

Counts

748 → 748

Iterations

Iter	Nodes
done	5000
2	3501
1	1566
0	692

prune4.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 21.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (/ 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))))
0.6b	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
2.6b	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite382.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`pow2` `pow-plus` `flip3--` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `frac-add`

Counts

4 → 364

Calls

4 calls:

183.0ms	(/ (- (* (/ 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)))))
87.0ms	(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
46.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
24.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series697.0ms

Counts

4 → 12

Calls

4 calls:

521.0ms	(/ (- (* (/ 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)))))
46.0ms	(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
33.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
97.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify2.2s

Counts

376 → 376

Iterations

Iter	Nodes
done	5000
1	1774
0	530

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt x))
0.3b	(/ (/ (- (* (* 1.0 (/ 1.0 (sqrt x))) (sqrt (+ x 1.0))) (* (sqrt x) (* (/ 1.0 (sqrt (+ x 1.0))) 1.0))) (* (sqrt x) (sqrt (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
2.7b	(- (* (* 1.0 (/ 1.0 (sqrt x))) (sqrt (+ x 1.0))) (* (sqrt x) (* (/ 1.0 (sqrt (+ x 1.0))) 1.0)))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

369×	`times-frac`
355×	`*-un-lft-identity`
143×	`sqrt-prod`
141×	`distribute-lft-out`
131×	`add-sqr-sqrt`
123×	`add-cube-cbrt`
42×	`associate-*r/`
37×	`div-inv`
36×	`sqrt-div`
33×	`associate-/r/`
20×	`associate-/r*`
19×	`flip3-+` `flip-+`
17×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/l*`
8×	`pow1`
7×	`associate-r`
6×	`cbrt-undiv` `div-exp` `associate-l` `associate-*l/` `add-log-exp`
5×	`frac-sub`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down`
2×	`frac-times` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod`
1×	`sub-neg` `flip3--` `fma-neg` `sqrt-unprod` `diff-log` `prod-diff` `frac-add` `*-commutative` `flip--` `associate-/l/`

Counts

4 → 269

Calls

4 calls:

5.0ms	(/ 1.0 (sqrt x))
186.0ms	(/ (/ (- (* (* 1.0 (/ 1.0 (sqrt x))) (sqrt (+ x 1.0))) (* (sqrt x) (* (/ 1.0 (sqrt (+ x 1.0))) 1.0))) (* (sqrt x) (sqrt (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
22.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
46.0ms	(- (* (* 1.0 (/ 1.0 (sqrt x))) (sqrt (+ x 1.0))) (* (sqrt x) (* (/ 1.0 (sqrt (+ x 1.0))) 1.0)))

series2.2s

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1.0 (sqrt x))
1.9s	(/ (/ (- (* (* 1.0 (/ 1.0 (sqrt x))) (sqrt (+ x 1.0))) (* (sqrt x) (* (/ 1.0 (sqrt (+ x 1.0))) 1.0))) (* (sqrt x) (sqrt (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
72.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
218.0ms	(- (* (* 1.0 (/ 1.0 (sqrt x))) (sqrt (+ x 1.0))) (* (sqrt x) (* (/ 1.0 (sqrt (+ x 1.0))) 1.0)))

simplify2.4s

Counts

281 → 281

Iterations

Iter	Nodes
done	5001
1	1448
0	499

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* (sqrt x) (sqrt (+ x 1.0)))) (* (sqrt x) (sqrt (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
2.2b	(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

678×	`times-frac`
541×	`*-un-lft-identity`
226×	`distribute-lft-out`
214×	`sqrt-prod`
185×	`add-sqr-sqrt`
169×	`add-cube-cbrt`
64×	`sqrt-div` `associate-*r/`
63×	`associate-/r/` `div-inv`
37×	`add-cbrt-cube` `add-exp-log`
33×	`flip3-+` `flip-+`
17×	`cbrt-undiv` `div-exp`
15×	`associate-/l*`
14×	`associate-/r` `associate-r*`
12×	`pow1` `associate-l`
8×	`unswap-sqr`
7×	`prod-exp` `cbrt-unprod`
6×	`pow-prod-down` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `log1p-expm1-u`
3×	`div-sub`
2×	`sqrt-unprod` `associate--l+` `*-commutative`
1×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3--` `fma-neg` `diff-log` `prod-diff` `frac-add` `flip--` `associate-/l/`

Counts

4 → 358

Calls

4 calls:

160.0ms	(/ (/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* (sqrt x) (sqrt (+ x 1.0)))) (* (sqrt x) (sqrt (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
21.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
20.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
31.0ms	(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

528.0ms	(/ (/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* (sqrt x) (sqrt (+ x 1.0)))) (* (sqrt x) (sqrt (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
63.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
63.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
4.0ms	(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

simplify1.5s

Counts

370 → 370

Iterations

Iter	Nodes
done	5001
1	1733
0	571

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

regimes61.0ms

Accuracy

0% (0.3b remaining)

Error of 5.5b against oracle of 5.1b and baseline of 5.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample1.8s

Algorithm

intervals

Results

394.0ms	8087×	body	80	nan
383.0ms	614×	body	320	valid
338.0ms	1863×	body	640	valid
259.0ms	1200×	body	1280	valid
207.0ms	4023×	body	80	valid
22.0ms	300×	body	160	valid