Details

sample41.0ms

Algorithm

intervals

Results

8.0ms	288×	body	80	nan
6.0ms	52×	body	640	valid
5.0ms	34×	body	1280	valid
5.0ms	142×	body	80	valid
2.0ms	22×	body	320	valid
0.0ms	6×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize26.0ms

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))
3.0b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite202.0ms

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` `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 → 758

Calls

4 calls:

6.0ms	(sqrt (+ x 1.0))
10.0ms	(/ 1.0 (sqrt (+ x 1.0)))
5.0ms	(/ 1.0 (sqrt x))
109.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ x 1.0))
130.0ms	(/ 1.0 (sqrt (+ x 1.0)))
70.0ms	(/ 1.0 (sqrt x))
213.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.4s

Counts

770 → 770

Iterations

Iter	Nodes
done	5000
2	4935
1	1587
0	702

prune2.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(* (sqrt (+ x 1.0)) (sqrt x))
3.0b	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `sqrt-prod`
11×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`pow1`
7×	`associate-l`
6×	`sqrt-div` `associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `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` `fma-neg` `sqrt-unprod` `diff-log` `div-sub` `prod-diff` `-commutative` `hypot-def` `div-inv`

Counts

4 → 98

Calls

4 calls:

12.0ms	(sqrt (+ x 1.0))
44.0ms	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt (+ x 1.0)) (sqrt x)))
25.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
14.0ms	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series646.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ x 1.0))
359.0ms	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt (+ x 1.0)) (sqrt x)))
93.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
154.0ms	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify1.5s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	2941
1	586
0	208

prune585.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0)))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(/ (/ (fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0)))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(* (sqrt (+ x 1.0)) (sqrt x))
3.2b	(fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0))))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
22×	`add-sqr-sqrt`
18×	`times-frac`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp` `associate-/l*`
11×	`sqrt-prod`
8×	`pow1` `associate-/r/`
7×	`associate-l` `prod-exp` `cbrt-unprod`
6×	`associate-r` `associate-*r/`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `sqrt-div` `associate-*l/` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down`
2×	`clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`sqrt-unprod` `*-commutative` `fma-udef` `distribute-lft-out` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

24.0ms	(/ (fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0)))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
49.0ms	(/ (/ (fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0)))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
39.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
1.0ms	(fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

290.0ms	(/ (fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0)))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
751.0ms	(/ (/ (fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0)))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
87.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
76.0ms	(fma (* 1.0 1.0) (+ x 1.0) (* x (- (* 1.0 1.0))))

simplify1.3s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	4071
1	739
0	263

prune601.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(* (sqrt (+ x 1.0)) (sqrt x))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
27×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
19×	`sqrt-prod`
18×	`times-frac`
16×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp` `associate-/l*`
8×	`pow1` `associate-/r/`
7×	`fma-def` `associate-l` `prod-exp` `cbrt-unprod`
6×	`flip3-+` `associate-r` `associate-*r/` `flip-+` `distribute-lft-out` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `associate-*l/` `log1p-expm1-u` `div-inv` `unswap-sqr`
3×	`pow-prod-down`
2×	`clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log` `sqrt-unprod` `*-commutative` `associate-/l/`

Counts

4 → 129

Calls

4 calls:

28.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
24.0ms	(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
44.0ms	(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
25.0ms	(* (sqrt (+ x 1.0)) (sqrt x))

series855.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
156.0ms	(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
554.0ms	(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
69.0ms	(* (sqrt (+ x 1.0)) (sqrt x))

simplify1.3s

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
2	4350
1	760
0	271

prune517.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes73.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample1.6s

Algorithm

intervals

Results

576.0ms	7906×	body	80	nan
257.0ms	1849×	body	640	valid
237.0ms	1118×	body	1280	valid
182.0ms	4066×	body	80	valid
62.0ms	668×	body	320	valid
50.0ms	299×	body	160	valid