Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	334×	body	80	nan
5.0ms	46×	body	1280	valid
4.0ms	50×	body	640	valid
3.0ms	130×	body	80	valid
1.0ms	16×	body	320	valid
1.0ms	14×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	6
done	14	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize11.0ms

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))
3.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite184.0ms

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-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--` `hypot-def`

Counts

4 → 758

Calls

4 calls:

8.0ms	(sqrt (+ x 1.0))
12.0ms	(/ 1.0 (sqrt (+ x 1.0)))
6.0ms	(/ 1.0 (sqrt x))
84.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ x 1.0))
70.0ms	(/ 1.0 (sqrt (+ x 1.0)))
43.0ms	(/ 1.0 (sqrt x))
133.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify229.0ms

Counts

770 → 770

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	1538	25021
1	4278	18390
2	5001	18355
done	5001	18355

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 19.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
3.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 151

Calls

4 calls:

8.0ms	(sqrt (+ x 1.0))
86.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
24.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
51.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series409.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1.0))
256.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
59.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
65.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify87.0ms

Counts

163 → 163

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	636	1812
1	2945	1369
2	5002	1271
done	5002	1271

prune338.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
2.4b	(+ x (- 1.0 x))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

112×	`*-un-lft-identity`
41×	`distribute-lft-out`
36×	`add-sqr-sqrt`
35×	`sqrt-prod`
31×	`times-frac`
29×	`add-exp-log` `add-cbrt-cube`
28×	`add-cube-cbrt`
11×	`associate-+r+`
9×	`cbrt-undiv` `div-exp` `prod-diff` `add-log-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `associate-/l*`
5×	`flip3-+` `associate-*r/` `flip-+`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `associate-/l/`
2×	`associate-+r-` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sum-log` `div-inv`
1×	`+-commutative` `sub-neg` `sqrt-unprod` `diff-log` `div-sub` `*-commutative`

Counts

4 → 156

Calls

4 calls:

84.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
57.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
24.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
16.0ms	(+ x (- 1.0 x))

series682.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
485.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
54.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify105.0ms

Counts

168 → 168

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	799	1711
1	4236	1448
2	5001	1435
done	5001	1435

prune405.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

34.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
42.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
46.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
25.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series938.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
129.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
687.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
55.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify86.0ms

Counts

143 → 143

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	704	1320
1	3636	1120
2	5002	1050
done	5002	1050

prune309.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	9
1	11	9
done	11	9

end0.0ms

sample864.0ms

Algorithm

intervals

Results

179.0ms	1894×	body	640	valid
159.0ms	8104×	body	80	nan
138.0ms	1147×	body	1280	valid
103.0ms	4054×	body	80	valid
41.0ms	600×	body	320	valid
14.0ms	305×	body	160	valid