Details

sample359.0ms

Algorithm

intervals

Results

19.0ms	735×	body	80	nan
5.0ms	256×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize9.0ms

Local error

Found 1 expressions with local error:

0.5b	(* (sqrt (- x 1.0)) (sqrt x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`sqrt-prod`
8×	`associate-l`
7×	`*-un-lft-identity`
6×	`associate-r`
5×	`pow1` `add-cube-cbrt`
4×	`unswap-sqr`
3×	`add-exp-log` `pow-prod-down` `add-cbrt-cube`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-*l/`
1×	`expm1-log1p-u` `flip3--` `sqrt-unprod` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`

Counts

1 → 36

Calls

1 calls:

27.0ms

(* (sqrt (- x 1.0)) (sqrt x))

series78.0ms

Counts

1 → 3

Calls

1 calls:

77.0ms

(* (sqrt (- x 1.0)) (sqrt x))

simplify76.0ms

Counts

39 → 39

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	188	226
1	635	215
2	2636	210
3	5002	210
done	5002	210

prune73.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize5.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune4.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

66×	`sqrt-prod`
40×	`add-sqr-sqrt`
36×	`sqrt-div`
24×	`*-un-lft-identity`
22×	`associate-l`
20×	`pow1`
16×	`add-cube-cbrt`
13×	`sqrt-pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow-prod-down` `associate-*l/`
9×	`flip3--` `pow1/2` `flip--`
7×	`associate-r`
6×	`unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `rem-sqrt-square` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`sqrt-unprod`
2×	`associate-r/` `-commutative`

Counts

4 → 130

Calls

4 calls:

8.0ms	(sqrt (sqrt (- x 1.0)))
9.0ms	(sqrt (sqrt (- x 1.0)))
69.0ms	(* (sqrt (sqrt (- x 1.0))) (* (sqrt (sqrt (- x 1.0))) (sqrt x)))
33.0ms	(* (sqrt (sqrt (- x 1.0))) (sqrt x))

series526.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(sqrt (sqrt (- x 1.0)))
100.0ms	(sqrt (sqrt (- x 1.0)))
66.0ms	(* (sqrt (sqrt (- x 1.0))) (* (sqrt (sqrt (- x 1.0))) (sqrt x)))
261.0ms	(* (sqrt (sqrt (- x 1.0))) (sqrt x))

simplify59.0ms

Counts

142 → 142

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	588	1126
1	2105	1021
2	5002	997
done	5002	997

prune319.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(sqrt (sqrt (- x 1.0)))
0.3b	(* (pow (- x 1.0) 1/4) (* (sqrt (sqrt (- x 1.0))) (sqrt x)))
0.3b	(* (sqrt (sqrt (- x 1.0))) (sqrt x))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

39×	`sqrt-prod`
32×	`add-sqr-sqrt`
20×	`associate-l`
18×	`add-exp-log` `*-un-lft-identity`
12×	`add-cube-cbrt` `sqrt-div`
10×	`prod-exp` `add-cbrt-cube`
9×	`pow1`
7×	`associate-r`
6×	`sqrt-pow1` `unswap-sqr`
5×	`unpow-prod-down`
4×	`pow1/2` `associate-*l/` `cbrt-unprod`
3×	`expm1-log1p-u` `flip3--` `pow-prod-down` `flip--` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`pow-to-exp` `rem-sqrt-square` `associate-r/` `pow-exp` `-commutative`
1×	`sqrt-unprod` `sqr-pow`

Counts

3 → 96

Calls

3 calls:

8.0ms	(sqrt (sqrt (- x 1.0)))
73.0ms	(* (pow (- x 1.0) 1/4) (* (sqrt (sqrt (- x 1.0))) (sqrt x)))
32.0ms	(* (sqrt (sqrt (- x 1.0))) (sqrt x))

series537.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(sqrt (sqrt (- x 1.0)))
171.0ms	(* (pow (- x 1.0) 1/4) (* (sqrt (sqrt (- x 1.0))) (sqrt x)))
264.0ms	(* (sqrt (sqrt (- x 1.0))) (sqrt x))

simplify67.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	668	911
1	2472	859
2	5001	840
done	5001	840

prune249.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes17.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3
done	9	3

end0.0ms

sample1.1s

Algorithm

intervals

Results

548.0ms	23430×	body	80	nan
151.0ms	7990×	body	80	valid
0.0ms	10×	body	160	valid