Details

sample43.0ms

Algorithm

intervals

Results

9.0ms	61×	body	1280	valid
7.0ms	245×	body	80	nan
4.0ms	135×	body	80	valid
4.0ms	37×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	10×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize13.0ms

Local error

Found 1 expressions with local error:

2.8b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `sqrt-prod`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 19

Calls

1 calls:

89.0ms

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

series106.0ms

Counts

1 → 3

Calls

1 calls:

106.0ms

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

simplify942.0ms

Counts

22 → 22

Iterations

Useful iterations: done (941.0ms)

Iter	Nodes	Cost
0	59	310
1	134	285
2	443	263
3	1777	257
done	5001	250

prune63.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
20×	`sqrt-prod` `distribute-lft-out`
18×	`times-frac`
13×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 55

Calls

2 calls:

34.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
52.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series266.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
187.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify689.0ms

Counts

61 → 61

Iterations

Useful iterations: done (682.0ms)

Iter	Nodes	Cost
0	128	947
1	308	865
2	1239	790
done	5001	782

prune264.0ms

Pruning

7 alts after pruning (6 fresh and 1 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))))

rewrite409.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
700×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
254×	`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-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 445

Calls

4 calls:

40.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
60.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
76.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
194.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series862.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
152.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
376.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
154.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify2.1s

Counts

457 → 457

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	440	15237
1	1066	12250
2	4063	11774
done	5002	11088

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3)))
0.3b	(cbrt (pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3))
0.4b	(pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3)

rewrite559.0ms

Algorithm

rewrite-expression-head

Rules

1804×	`*-un-lft-identity`
1674×	`times-frac`
1600×	`sqrt-prod`
840×	`cbrt-prod`
684×	`add-sqr-sqrt` `add-cube-cbrt`
640×	`distribute-lft-out`
324×	`unpow-prod-down` `cube-prod`
64×	`sqrt-div`
60×	`associate-/r/`
36×	`cube-mult` `unpow3` `associate-/r` `associate-/l` `sqr-pow`
32×	`flip3-+` `flip-+`
30×	`div-inv`
12×	`add-exp-log`
10×	`add-cbrt-cube`
6×	`pow1` `cube-div`
4×	`cbrt-undiv` `cbrt-div` `div-exp` `add-log-exp`
3×	`pow-unpow` `pow-pow`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `associate-/l/` `rem-cube-cbrt`

Counts

4 → 1096

Calls

4 calls:

61.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
247.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3)))
58.0ms	(cbrt (pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3))
45.0ms	(pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3)

series1.4s

Counts

4 → 12

Calls

4 calls:

376.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
389.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3)))
187.0ms	(cbrt (pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3))
480.0ms	(pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3)

simplify1.4s

Counts

1108 → 1108

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	865	46917
1	2231	35989
done	5000	30201

prune1.8s

Pruning

8 alts after pruning (6 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

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	9	9
done	9	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

786.0ms	1664×	body	1280	valid
319.0ms	7921×	body	80	nan
264.0ms	1273×	body	640	valid
199.0ms	4141×	body	80	valid
63.0ms	611×	body	320	valid
22.0ms	311×	body	160	valid