Details

sample30.0ms

Algorithm

intervals

Results

7.0ms	278×	body	80	nan
5.0ms	64×	body	1280	valid
3.0ms	48×	body	640	valid
2.0ms	114×	body	80	valid
1.0ms	21×	body	320	valid
0.0ms	9×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize5.0ms

Local error

Found 1 expressions with local error:

2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

57×	`sqrt-prod`
50×	`*-un-lft-identity`
42×	`prod-diff`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`fma-neg`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 70

Calls

1 calls:

54.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series68.0ms

Counts

1 → 3

Calls

1 calls:

68.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify133.0ms

Counts

73 → 73

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	252	1065
1	759	733
2	4363	623
3	5001	593
done	5001	593

prune97.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
32×	`distribute-lft-out`
28×	`sqrt-prod`
24×	`times-frac`
16×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 75

Calls

2 calls:

37.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
60.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series202.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
136.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify43.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	356	693
1	1446	627
2	5001	586
done	5001	586

prune170.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite353.0ms

Algorithm

rewrite-expression-head

Rules

1122×	`*-un-lft-identity`
908×	`sqrt-prod`
774×	`times-frac`
460×	`distribute-lft-out`
310×	`add-sqr-sqrt`
292×	`add-cube-cbrt`
46×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
15×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
8×	`hypot-def`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 563

Calls

4 calls:

44.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
44.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
61.0ms	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
145.0ms	(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series802.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
165.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
334.0ms	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
138.0ms	(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify154.0ms

Counts

575 → 575

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1107	11444
1	4551	9783
2	5001	9783
done	5001	9783

prune658.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.4b	(pow (sqrt x) 3/2)
0.5b	(* (sqrt x) (sqrt x))
2.1b	(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `sqrt-prod`
37×	`*-un-lft-identity`
36×	`pow1`
23×	`add-cube-cbrt`
19×	`swap-sqr`
17×	`sqrt-pow1` `pow1/2`
13×	`associate-r` `associate-l`
12×	`sqrt-div`
10×	`pow-prod-up`
9×	`add-exp-log`
8×	`add-cbrt-cube` `unswap-sqr`
6×	`unpow-prod-down` `flip3-+` `pow-prod-down` `pow-sqr` `flip-+` `distribute-lft-out` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`pow-unpow` `pow-pow`
2×	`pow2` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`
1×	`pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `fma-neg` `diff-log` `prod-diff` `pow-exp` `sqrt-pow2` `flip--` `sqr-pow`

Counts

4 → 157

Calls

4 calls:

44.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
4.0ms	(pow (sqrt x) 3/2)
13.0ms	(* (sqrt x) (sqrt x))
14.0ms	(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
113.0ms	(pow (sqrt x) 3/2)
16.0ms	(* (sqrt x) (sqrt x))
89.0ms	(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))

simplify87.0ms

Counts

169 → 169

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	503	743
1	2458	632
2	5002	611
done	5002	611

prune522.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes45.0ms

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	6
1	16	6
2	16	6
done	16	6

end0.0ms

sample703.0ms

Algorithm

intervals

Results

137.0ms	1691×	body	1280	valid
132.0ms	8018×	body	80	nan
86.0ms	1335×	body	640	valid
70.0ms	4048×	body	80	valid
29.0ms	618×	body	320	valid
10.0ms	308×	body	160	valid