Details

sample60.0ms

Algorithm

intervals

Results

12.0ms	272×	body	80	nan
11.0ms	59×	body	640	valid
10.0ms	41×	body	1280	valid
6.0ms	123×	body	80	valid
3.0ms	19×	body	320	valid
1.0ms	14×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.0b

localize123.0ms

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))))

rewrite557.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
879×	`*-un-lft-identity`
747×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
566×	`sqrt-prod`
74×	`distribute-lft-out`
54×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `hypot-def` `flip--`

Counts

4 → 762

Calls

4 calls:

16.0ms	(sqrt (+ x 1.0))
47.0ms	(/ 1.0 (sqrt (+ x 1.0)))
23.0ms	(/ 1.0 (sqrt x))
199.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ x 1.0))
145.0ms	(/ 1.0 (sqrt (+ x 1.0)))
57.0ms	(/ 1.0 (sqrt x))
244.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify6.5s

Counts

774 → 774

Iterations

Iter	Nodes
done	5000
2	3569
1	1591
0	706

prune5.8s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 19.3b

localize202.0ms

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)))))

rewrite716.0ms

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` `insert-posit16` `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 → 368

Calls

4 calls:

330.0ms	(/ (- (* (/ 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)))))
157.0ms	(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
99.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
53.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series690.0ms

Counts

4 → 12

Calls

4 calls:

512.0ms	(/ (- (* (/ 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)))))
31.0ms	(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
43.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
103.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify4.7s

Counts

380 → 380

Iterations

Iter	Nodes
done	5001
1	1793
0	534

prune3.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize211.0ms

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)))

rewrite334.0ms

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×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u`
3×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`
2×	`associate-l/` `associate-r/`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--`

Counts

4 → 186

Calls

4 calls:

79.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
28.0ms	(* (sqrt x) (sqrt x))
29.0ms	(* (sqrt x) (sqrt x))
186.0ms	(- (* (* 1.0 1.0) (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))) (* (* (sqrt x) (sqrt x)) (* 1.0 1.0)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
19.0ms	(* (sqrt x) (sqrt x))
20.0ms	(* (sqrt x) (sqrt x))
24.0ms	(- (* (* 1.0 1.0) (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))) (* (* (sqrt x) (sqrt x)) (* 1.0 1.0)))

simplify2.4s

Counts

198 → 198

Iterations

Iter	Nodes
done	5001
2	1311
1	401
0	161

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.6b

localize121.0ms

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)))))

rewrite728.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `*-commutative`
1×	`frac-add` `associate-/l/`

Counts

4 → 423

Calls

4 calls:

76.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
27.0ms	(* (sqrt x) (sqrt x))
155.0ms	(/ 1.0 (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))))
373.0ms	(/ (/ 1.0 (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

series671.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
18.0ms	(* (sqrt x) (sqrt x))
60.0ms	(/ 1.0 (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))))
572.0ms	(/ (/ 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

435 → 435

Iterations

Iter	Nodes
done	5000
1	1715
0	576

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes157.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	20
1	20
0	15

end0.0ms

sample2.2s

Algorithm

intervals

Results

690.0ms	1852×	body	640	valid
426.0ms	8083×	body	80	nan
336.0ms	1185×	body	1280	valid
250.0ms	4040×	body	80	valid
136.0ms	605×	body	320	valid
31.0ms	318×	body	160	valid