Details

sample104.0ms

Algorithm

intervals

Results

27.0ms	66×	body	640	valid
22.0ms	249×	body	80	nan
18.0ms	32×	body	1280	valid
13.0ms	121×	body	80	valid
6.0ms	20×	body	320	valid
3.0ms	17×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	17
2	17
1	13
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
4.4b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite94.0ms

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:

10.0ms	(sqrt (+ x 1))
16.0ms	(/ 1 (sqrt (+ x 1)))
11.0ms	(/ 1 (sqrt x))
34.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series221.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1))
36.0ms	(/ 1 (sqrt (+ x 1)))
50.0ms	(/ 1 (sqrt x))
106.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify1.2s

Counts

805 → 805

Iterations

Iter	Nodes
2	2402
1	1415
0	651

prune9.6s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 20.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.3b	(* (sqrt x) (sqrt (+ x 1)))
4.4b	(- (sqrt (+ x 1)) (sqrt x))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

88×	`sqrt-prod`
79×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
42×	`prod-diff`
39×	`add-cube-cbrt`
12×	`distribute-lft-out` `difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log`
10×	`times-frac` `associate-/l*`
9×	`pow1` `distribute-lft-out--`
7×	`fma-neg` `associate-r`
6×	`sqrt-div` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `hypot-def` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-unprod` `diff-log` `div-sub` `-commutative` `div-inv`

Counts

4 → 171

Calls

4 calls:

11.0ms	(sqrt (+ x 1))
110.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
34.0ms	(* (sqrt x) (sqrt (+ x 1)))
63.0ms	(- (sqrt (+ x 1)) (sqrt x))

series419.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ x 1))
228.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
93.0ms	(* (sqrt x) (sqrt (+ x 1)))
64.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify9.9s

Counts

183 → 183

Iterations

Iter	Nodes
3	9865
2	1818
1	524
0	216

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.3b	(* (sqrt x) (sqrt (+ x 1)))
0.3b	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

122×	`*-un-lft-identity`
78×	`times-frac`
59×	`sqrt-prod`
49×	`add-sqr-sqrt`
46×	`distribute-lft-out`
41×	`add-cube-cbrt`
32×	`add-exp-log`
27×	`associate-/l*`
20×	`add-cbrt-cube`
14×	`div-exp`
9×	`pow1`
8×	`associate-/r/`
7×	`cbrt-undiv` `associate-/r` `fma-def` `associate-r*`
6×	`flip3-+` `associate-l` `flip-+` `add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `sqrt-div` `associate-*r/` `insert-posit16` `log1p-expm1-u` `div-inv` `unswap-sqr`
3×	`rec-exp` `1-exp` `pow-prod-down` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log` `sqrt-unprod` `*-commutative` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 185

Calls

4 calls:

32.0ms	(+ (sqrt (+ x 1)) (sqrt x))
28.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
16.0ms	(* (sqrt x) (sqrt (+ x 1)))
67.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))

series494.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(+ (sqrt (+ x 1)) (sqrt x))
92.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
66.0ms	(* (sqrt x) (sqrt (+ x 1)))
262.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))

simplify2.4s

Counts

197 → 197

Iterations

Iter	Nodes
3	5470
2	1580
1	570
0	234

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (fma (sqrt x) (sqrt (+ x 1)) (+ x 1)))
0.0b	(fma (sqrt x) (sqrt (+ x 1)) (+ x 1))
0.1b	(* (/ 1 (sqrt x)) (/ 1 (fma (sqrt x) (sqrt (+ x 1)) (+ x 1))))
0.3b	(/ 1 (sqrt x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
76×	`times-frac`
58×	`*-un-lft-identity`
52×	`add-exp-log`
47×	`add-cube-cbrt`
27×	`sqrt-prod`
22×	`associate-l`
20×	`add-cbrt-cube` `div-exp`
16×	`prod-exp`
15×	`unswap-sqr`
13×	`associate-r`
11×	`pow1`
10×	`rec-exp` `1-exp`
9×	`associate-/r*`
6×	`cbrt-undiv` `pow-flip` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `inv-pow` `add-log-exp`
3×	`pow-prod-down`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `fma-udef`

Counts

4 → 181

Calls

4 calls:

4.0ms	(/ 1 (fma (sqrt x) (sqrt (+ x 1)) (+ x 1)))
0.0ms	(fma (sqrt x) (sqrt (+ x 1)) (+ x 1))
17.0ms	(* (/ 1 (sqrt x)) (/ 1 (fma (sqrt x) (sqrt (+ x 1)) (+ x 1))))
5.0ms	(/ 1 (sqrt x))

series419.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ 1 (fma (sqrt x) (sqrt (+ x 1)) (+ x 1)))
76.0ms	(fma (sqrt x) (sqrt (+ x 1)) (+ x 1))
208.0ms	(* (/ 1 (sqrt x)) (/ 1 (fma (sqrt x) (sqrt (+ x 1)) (+ x 1))))
35.0ms	(/ 1 (sqrt x))

simplify1.1s

Counts

193 → 193

Iterations

Iter	Nodes
3	3192
2	1373
1	573
0	222

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	14
1	14
0	10

end0.0ms

sample2.3s

Algorithm

intervals

Results

847.0ms	1847×	body	640	valid
455.0ms	7978×	body	80	nan
402.0ms	1132×	body	1280	valid
286.0ms	4106×	body	80	valid
127.0ms	605×	body	320	valid
36.0ms	310×	body	160	valid