Details

sample56.0ms

Algorithm

intervals

Results

12.0ms	60×	body	1280	valid
10.0ms	238×	body	80	nan
7.0ms	41×	body	640	valid
5.0ms	123×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	8×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize14.0ms

Local error

Found 1 expressions with local error:

2.7b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite53.0ms

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×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--`

Counts

1 → 70

Calls

1 calls:

50.0ms

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

series76.0ms

Counts

1 → 3

Calls

1 calls:

76.0ms

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

simplify1.9s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
3	1899
2	630
1	272
0	119

prune152.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 83

Calls

2 calls:

33.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
119.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))

series347.0ms

Counts

2 → 6

Calls

2 calls:

113.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
233.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.9s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
3	3761
2	1167
1	390
0	150

prune373.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite692.0ms

Algorithm

rewrite-expression-head

Rules

1133×	`*-un-lft-identity`
638×	`sqrt-prod`
468×	`distribute-lft-out`
377×	`times-frac`
145×	`add-sqr-sqrt`
121×	`swap-sqr`
114×	`add-cube-cbrt`
92×	`distribute-lft-out--`
39×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `unswap-sqr`
7×	`div-inv`
5×	`sqrt-div` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `associate-+r-` `frac-2neg` `div-sub` `div-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 408

Calls

4 calls:

83.0ms	(sqrt (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x))))
114.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
89.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
371.0ms	(* (sqrt (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

477.0ms	(sqrt (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x))))
192.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
220.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
203.0ms	(* (sqrt (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify2.6s

Counts

420 → 420

Iterations

Iter	Nodes
done	5001
2	2170
1	776
0	330

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

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

rewrite387.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
708×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
270×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-cbrt-cube` `add-exp-log`
8×	`hypot-def`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 461

Calls

4 calls:

75.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
40.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
59.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
152.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

198.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
217.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
481.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
215.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify2.1s

Counts

473 → 473

Iterations

Iter	Nodes
done	5000
2	2669
1	1075
0	448

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes68.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end1.0ms

sample1.8s

Algorithm

intervals

Results

577.0ms	4033×	body	80	valid
348.0ms	1784×	body	1280	valid
334.0ms	8087×	body	80	nan
153.0ms	1272×	body	640	valid
63.0ms	293×	body	160	valid
56.0ms	618×	body	320	valid