Details

sample24.0ms

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

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

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:

4.0ms	(sqrt (+ x 1.0))
25.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series107.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(sqrt (+ x 1.0))
76.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.0s

Counts

95 → 95

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	137	1993
1	295	1432
2	772	1124
3	3842	950
done	5000	943

prune133.0ms

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
33×	`distribute-lft-out`
32×	`sqrt-prod`
24×	`times-frac`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
7×	`fma-def`
6×	`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 → 94

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
17.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
30.0ms	(/ (+ 0 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series250.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(sqrt (+ x 1.0))
64.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
150.0ms	(/ (+ 0 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify526.0ms

Counts

103 → 103

Iterations

Useful iterations: done (523.0ms)

Iter	Nodes	Cost
0	169	1453
1	409	1180
2	1303	1091
done	5001	1085

prune213.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

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 1.0)) (sqrt x))))
23.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
21.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
115.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series834.0ms

Counts

4 → 12

Calls

4 calls:

360.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
150.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
149.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
174.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.2s

Counts

270 → 270

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	317	6276
1	676	4462
2	2745	4194
done	5001	4187

prune534.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b	(/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(pow (/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) 1/2)
0.3b	(* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
32×	`sqrt-prod`
31×	`add-exp-log`
29×	`distribute-lft-out`
19×	`flip3-+` `flip-+`
18×	`add-cbrt-cube`
16×	`associate-/r/`
14×	`add-sqr-sqrt`
13×	`unpow-prod-down`
12×	`pow1` `frac-times` `add-cube-cbrt`
10×	`swap-sqr`
9×	`prod-exp`
8×	`div-exp`
7×	`fma-def`
6×	`associate-r/` `associate-r` `associate-l` `associate-l/` `add-log-exp`
5×	`pow-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow`
2×	`times-frac` `div-inv`
1×	`+-commutative` `pow2` `distribute-rgt-in` `pow-to-exp` `pow-pow` `frac-2neg` `distribute-lft-in` `pow-plus` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `pow-sqr` `-commutative` `pow-prod-up` `associate-/l*` `unpow1/2` `unswap-sqr` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

19.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
27.0ms	(/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x))))
32.0ms	(pow (/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) 1/2)
99.0ms	(* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))

series960.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
193.0ms	(/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x))))
585.0ms	(pow (/ (* 1.0 1.0) (* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) 1/2)
110.0ms	(* (+ (sqrt (+ x 1.0)) (sqrt x)) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.2s

Counts

150 → 150

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	267	3700
1	787	3109
2	3193	2450
done	5000	2443

prune332.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes21.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	15	25
done	15	25

end0.0ms

sample672.0ms

Algorithm

intervals

Results

149.0ms	1723×	body	1280	valid
144.0ms	7968×	body	80	nan
81.0ms	1228×	body	640	valid
79.0ms	4137×	body	80	valid
30.0ms	606×	body	320	valid
10.0ms	306×	body	160	valid