Details

sample286.0ms

Algorithm

intervals

Results

20.0ms	797×	body	80	nan
5.0ms	255×	body	80	valid
0.0ms	1×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite17.0ms

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×	`flip3--` `sqrt-unprod` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `add-log-exp` `difference-of-squares`

Counts

1 → 34

Calls

1 calls:

15.0ms

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

series83.0ms

Counts

1 → 3

Calls

1 calls:

83.0ms

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

simplify2.7s

Counts

37 → 37

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	83	387
1	182	356
2	451	338
3	1104	335
4	2909	334
done	5000	332

prune74.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(- x (+ 0.5 (/ 0.125 x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity` `add-log-exp`
3×	`add-sqr-sqrt`
2×	`diff-log` `distribute-lft-out--`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `sum-log` `add-cbrt-cube` `flip--` `distribute-lft-out` `associate--r+` `difference-of-squares`

Counts

1 → 17

Calls

1 calls:

17.0ms

(- x (+ 0.5 (/ 0.125 x)))

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(- x (+ 0.5 (/ 0.125 x)))

simplify1.4s

Counts

20 → 20

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	42	229
1	102	220
2	243	200
3	764	200
4	2958	200
done	5001	200

prune33.0ms

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)))
0.2b	(* (sqrt (sqrt (- x 1.0))) (* (sqrt (sqrt (- x 1.0))) (sqrt x)))
0.4b	(* (sqrt (sqrt (- x 1.0))) (sqrt x))

rewrite67.0ms

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×	`frac-times` `rem-sqrt-square` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`sqrt-unprod`
2×	`associate-r/` `-commutative`

Counts

4 → 122

Calls

4 calls:

4.0ms	(sqrt (sqrt (- x 1.0)))
4.0ms	(sqrt (sqrt (- x 1.0)))
37.0ms	(* (sqrt (sqrt (- x 1.0))) (* (sqrt (sqrt (- x 1.0))) (sqrt x)))
17.0ms	(* (sqrt (sqrt (- x 1.0))) (sqrt x))

series557.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(sqrt (sqrt (- x 1.0)))
103.0ms	(sqrt (sqrt (- x 1.0)))
69.0ms	(* (sqrt (sqrt (- x 1.0))) (* (sqrt (sqrt (- x 1.0))) (sqrt x)))
280.0ms	(* (sqrt (sqrt (- x 1.0))) (sqrt x))

simplify1.1s

Counts

134 → 134

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	231	1970
1	565	1661
2	1584	1523
done	5001	1495

prune303.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (- x 1.0)))
0.2b	(* (sqrt (- x 1.0)) x)
0.2b	(* (sqrt (sqrt (- x 1.0))) (pow (* (sqrt (- x 1.0)) x) (/ 1 2)))
22.6b	(pow (* (sqrt (- x 1.0)) x) (/ 1 2))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
39×	`sqrt-prod`
26×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`associate-l`
17×	`add-exp-log`
13×	`pow-unpow`
12×	`pow1`
10×	`sqrt-div`
9×	`times-frac`
8×	`associate-r` `add-cbrt-cube` `unswap-sqr`
7×	`prod-exp`
5×	`sqrt-pow1` `sqr-pow`
4×	`associate-*l/` `pow-exp` `add-log-exp`
3×	`flip3--` `pow-prod-down` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `pow-pow` `pow1/2` `*-commutative` `cbrt-unprod`
1×	`div-inv`

Counts

4 → 114

Calls

4 calls:

4.0ms	(sqrt (sqrt (- x 1.0)))
13.0ms	(* (sqrt (- x 1.0)) x)
19.0ms	(* (sqrt (sqrt (- x 1.0))) (pow (* (sqrt (- x 1.0)) x) (/ 1 2)))
6.0ms	(pow (* (sqrt (- x 1.0)) x) (/ 1 2))

series494.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(sqrt (sqrt (- x 1.0)))
90.0ms	(* (sqrt (- x 1.0)) x)
72.0ms	(* (sqrt (sqrt (- x 1.0))) (pow (* (sqrt (- x 1.0)) x) (/ 1 2)))
222.0ms	(pow (* (sqrt (- x 1.0)) x) (/ 1 2))

simplify972.0ms

Counts

126 → 126

Iterations

Useful iterations: done (969.0ms)

Iter	Nodes	Cost
0	283	1966
1	670	1655
2	1877	1585
done	5001	1581

prune299.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes13.0ms

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	6	7
1	7	7
done	7	7

end0.0ms

sample1.1s

Algorithm

intervals

Results

577.0ms	23802×	body	80	nan
154.0ms	7989×	body	80	valid
0.0ms	11×	body	160	valid