Details

sample32.0ms

Algorithm

intervals

Results

6.0ms	286×	body	80	nan
6.0ms	59×	body	640	valid
5.0ms	41×	body	1280	valid
3.0ms	123×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	11×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	11
1	11	11
2	14	11
done	14	11

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
3.2b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite163.0ms

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:

4.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
3.0ms	(/ 1.0 (sqrt x))
70.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ x 1.0))
80.0ms	(/ 1.0 (sqrt (+ x 1.0)))
47.0ms	(/ 1.0 (sqrt x))
139.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.6s

Counts

770 → 770

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	701	40764
1	1517	36194
2	3581	26908
done	5000	26804

prune983.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.4b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
3.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite112.0ms

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:

4.0ms	(sqrt (+ x 1.0))
55.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
18.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
29.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series464.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ x 1.0))
282.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
66.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
77.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.1s

Counts

163 → 163

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	241	3181
1	637	2542
2	2430	1975
done	5000	1965

prune336.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (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)

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

19.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
42.0ms	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
14.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
23.0ms	(- (+ x 1.0) x)

series646.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
514.0ms	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
62.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(- (+ x 1.0) x)

simplify1.3s

Counts

135 → 135

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	254	2326
1	707	2032
2	2947	1608
done	5001	1587

prune489.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

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)))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
0.3b	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

rewrite87.0ms

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:

19.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
25.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
14.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
25.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

series755.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
145.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
56.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
486.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify1.3s

Counts

143 → 143

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	258	2403
1	704	2191
2	2798	1814
done	5000	1804

prune291.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	19	26
done	19	26

end0.0ms

sample819.0ms

Algorithm

intervals

Results

180.0ms	1796×	body	640	valid
160.0ms	8031×	body	80	nan
138.0ms	1162×	body	1280	valid
102.0ms	4077×	body	80	valid
42.0ms	609×	body	320	valid
17.0ms	356×	body	160	valid