Details

sample103.0ms

Algorithm

intervals

Results

26.0ms	64×	body	640	valid
23.0ms	246×	body	80	nan
16.0ms	31×	body	1280	valid
14.0ms	128×	body	80	valid
5.0ms	19×	body	320	valid
3.0ms	14×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	17
2	17
1	13
0	8

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
3.9b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

1063×	`times-frac`
902×	`*-un-lft-identity`
788×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
580×	`sqrt-prod`
74×	`distribute-lft-out`
56×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
25×	`difference-of-squares`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*` `distribute-lft-out--`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube`
6×	`pow-flip` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `hypot-def` `inv-pow`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 793

Calls

4 calls:

5.0ms	(sqrt (+ x 1))
9.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))
45.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt (+ x 1))
30.0ms	(/ 1 (sqrt (+ x 1)))
38.0ms	(/ 1 (sqrt x))
101.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify1.0s

Counts

805 → 805

Iterations

Iter	Nodes
2	2402
1	1415
0	651

prune9.1s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 20.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
0.3b	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.5b	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
3.9b	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

rewrite182.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`pow2` `pow-plus` `flip3--` `*-commutative` `flip--`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `frac-add`

Counts

4 → 486

Calls

4 calls:

37.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
91.0ms	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
25.0ms	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
17.0ms	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

series229.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
137.0ms	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
32.0ms	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
45.0ms	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

simplify2.9s

Counts

498 → 498

Iterations

Iter	Nodes
2	4732
1	1619
0	524

prune5.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.5b

localize67.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
0.3b	(/ (/ (- (+ x 1) x) (+ x (* x x))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
3.4b	(- (+ x 1) x)

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

1979×	`*-un-lft-identity`
1791×	`times-frac`
686×	`distribute-lft-out`
678×	`add-sqr-sqrt`
506×	`add-cube-cbrt`
472×	`sqrt-prod`
172×	`distribute-lft-out--`
168×	`div-inv`
102×	`distribute-rgt-out` `distribute-rgt1-in`
86×	`difference-of-squares`
42×	`associate-/l*`
39×	`associate-/r/`
29×	`associate-/r*`
19×	`flip3-+` `flip-+`
17×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`prod-diff`
9×	`add-log-exp`
8×	`pow1`
7×	`div-exp`
6×	`pow-flip`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `fma-neg` `insert-posit16` `log1p-expm1-u`
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` `associate--l+` `flip--` `associate-/l/`

Counts

4 → 788

Calls

4 calls:

10.0ms	(/ 1 (sqrt (+ x 1)))
7.0ms	(/ 1 (sqrt x))
94.0ms	(/ (/ (- (+ x 1) x) (+ x (* x x))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
59.0ms	(- (+ x 1) x)

series324.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1 (sqrt (+ x 1)))
49.0ms	(/ 1 (sqrt x))
221.0ms	(/ (/ (- (+ x 1) x) (+ x (* x x))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
2.0ms	(- (+ x 1) x)

simplify2.8s

Counts

800 → 800

Iterations

Iter	Nodes
2	4661
1	1872
0	707

prune6.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
0.4b	(/ 1 (+ x (* x x)))
4.3b	(/ (/ 1 (+ x (* x x))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

1041×	`times-frac`
965×	`*-un-lft-identity`
356×	`distribute-lft-out`
352×	`add-sqr-sqrt` `add-cube-cbrt`
292×	`sqrt-prod`
109×	`div-inv`
55×	`distribute-rgt-out` `distribute-rgt1-in`
41×	`associate-/r/`
34×	`associate-/r*`
30×	`associate-/l*`
25×	`add-exp-log`
20×	`flip3-+` `flip-+`
15×	`add-cbrt-cube`
12×	`div-exp`
9×	`pow1`
7×	`pow-flip`
6×	`cbrt-undiv`
4×	`expm1-log1p-u` `rec-exp` `clear-num` `frac-2neg` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`inv-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div`
1×	`frac-add` `associate-/l/`

Counts

4 → 542

Calls

4 calls:

9.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))
7.0ms	(/ 1 (+ x (* x x)))
49.0ms	(/ (/ 1 (+ x (* x x))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

series228.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (sqrt (+ x 1)))
34.0ms	(/ 1 (sqrt x))
20.0ms	(/ 1 (+ x (* x x)))
144.0ms	(/ (/ 1 (+ x (* x x))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

simplify1.2s

Counts

554 → 554

Iterations

Iter	Nodes
2	2869
1	1385
0	565

prune3.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes46.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	16
1	16
0	11

end0.0ms

sample2.3s

Algorithm

intervals

Results

496.0ms	1777×	body	640	valid
471.0ms	8213×	body	80	nan
361.0ms	1108×	body	1280	valid
343.0ms	337×	body	160	valid
342.0ms	4162×	body	80	valid
148.0ms	616×	body	320	valid