Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	275×	body	80	nan
4.0ms	44×	body	1280	valid
3.0ms	45×	body	640	valid
3.0ms	140×	body	80	valid
1.0ms	14×	body	320	valid
0.0ms	13×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `hypot-def`

Counts

2 → 89

Calls

2 calls:

5.0ms	(sqrt (+ x 1.0))
28.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series111.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(sqrt (+ x 1.0))
74.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify3.3s

Counts

95 → 95

Iterations

Useful iterations: 3 (528.0ms)

Iter	Nodes	Cost
0	137	1993
1	309	1467
2	918	1124
3	4514	950
done	5000	950

prune157.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt x) (sqrt (+ x 1.0)))
0.1b	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
32×	`distribute-lft-out`
31×	`sqrt-prod`
24×	`times-frac`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
6×	`fma-def` `associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 93

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
12.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
30.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

series244.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (+ x 1.0))
67.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
147.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify665.0ms

Counts

102 → 102

Iterations

Useful iterations: done (663.0ms)

Iter	Nodes	Cost
0	169	1453
1	413	1200
2	1507	1090
done	5000	1084

prune210.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 258

Calls

4 calls:

24.0ms	(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
21.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
23.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
116.0ms	(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

634.0ms	(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
170.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
151.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
175.0ms	(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

simplify1.7s

Counts

270 → 270

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	317	6276
1	684	4534
2	3276	4194
done	5001	4187

prune578.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
44×	`sqrt-prod`
28×	`distribute-lft-out`
19×	`flip3-+` `flip-+`
18×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r/`
14×	`add-sqr-sqrt`
12×	`pow1` `frac-times`
11×	`add-cube-cbrt`
10×	`swap-sqr`
6×	`fma-def` `associate-r/` `associate-r` `associate-l` `associate-l/` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`times-frac`
2×	`rem-sqrt-square` `div-inv`
1×	`+-commutative` `pow2` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `pow-sqr` `-commutative` `pow-prod-up` `associate-/l*` `unswap-sqr`

Counts

4 → 130

Calls

4 calls:

11.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
28.0ms	(/ (* 1.0 1.0) (* (+ (sqrt x) (sqrt (+ x 1.0))) (+ (sqrt x) (sqrt (+ x 1.0)))))
27.0ms	(sqrt (/ (* 1.0 1.0) (* (+ (sqrt x) (sqrt (+ x 1.0))) (+ (sqrt x) (sqrt (+ x 1.0))))))
88.0ms	(* (+ (sqrt x) (sqrt (+ x 1.0))) (+ (sqrt x) (sqrt (+ x 1.0))))

series560.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
191.0ms	(/ (* 1.0 1.0) (* (+ (sqrt x) (sqrt (+ x 1.0))) (+ (sqrt x) (sqrt (+ x 1.0)))))
193.0ms	(sqrt (/ (* 1.0 1.0) (* (+ (sqrt x) (sqrt (+ x 1.0))) (+ (sqrt x) (sqrt (+ x 1.0))))))
106.0ms	(* (+ (sqrt x) (sqrt (+ x 1.0))) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify937.0ms

Counts

142 → 142

Iterations

Useful iterations: done (933.0ms)

Iter	Nodes	Cost
0	233	3380
1	662	2828
2	2755	2261
done	5000	2252

prune367.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	12	20
done	12	20

end0.0ms

sample666.0ms

Algorithm

intervals

Results

145.0ms	1723×	body	1280	valid
138.0ms	7968×	body	80	nan
84.0ms	1228×	body	640	valid
81.0ms	4137×	body	80	valid
29.0ms	606×	body	320	valid
10.0ms	306×	body	160	valid