Details

sample61.0ms

Algorithm

intervals

Results

9.0ms	54×	body	1280	valid
9.0ms	251×	body	80	nan
5.0ms	135×	body	80	valid
5.0ms	37×	body	640	valid
2.0ms	21×	body	320	valid
1.0ms	9×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.3b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

12.0ms	(sqrt (+ x 1.0))
61.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series131.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(sqrt (+ x 1.0))
91.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.3s

Counts

41 → 41

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	84	488
1	183	440
2	432	410
3	1028	402
4	2702	390
done	5000	382

prune85.0ms

Pruning

2 alts after pruning (2 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	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

7.0ms	(sqrt (+ x 1.0))
46.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
56.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series329.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(sqrt (+ x 1.0))
105.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
178.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.9s

Counts

80 → 80

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	152	1125
1	343	1018
2	891	935
3	2607	919
done	5000	915

prune167.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

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)))
0.1b	(/ 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))))

rewrite390.0ms

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:

53.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
53.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
65.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
164.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.0s

Counts

4 → 12

Calls

4 calls:

199.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
217.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
398.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
200.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify1.8s

Counts

457 → 457

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	440	15237
1	1031	12250
2	2208	11576
done	5000	10949

prune918.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (sqrt (+ x 1.0)))
0.3b	(cbrt (sqrt (+ x 1.0)))
0.3b	(cbrt (sqrt (+ x 1.0)))
0.3b	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cbrt-prod`
44×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`sqrt-prod`
22×	`add-cube-cbrt`
18×	`cbrt-div` `sqrt-div`
14×	`swap-sqr`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out` `unswap-sqr`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 120

Calls

4 calls:

10.0ms	(cbrt (sqrt (+ x 1.0)))
9.0ms	(cbrt (sqrt (+ x 1.0)))
9.0ms	(cbrt (sqrt (+ x 1.0)))
67.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))

series501.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (sqrt (+ x 1.0)))
134.0ms	(cbrt (sqrt (+ x 1.0)))
119.0ms	(cbrt (sqrt (+ x 1.0)))
120.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))

simplify1.9s

Counts

132 → 132

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	172	2150
1	356	1967
2	910	1880
3	2298	1693
done	5000	1557

prune393.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes31.0ms

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

sample1.5s

Algorithm

intervals

Results

409.0ms	1737×	body	1280	valid
314.0ms	8028×	body	80	nan
197.0ms	1307×	body	640	valid
128.0ms	4108×	body	80	valid
94.0ms	574×	body	320	valid
16.0ms	274×	body	160	valid