Details

sample337.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
7.0ms	238×	body	80	nan

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	11
1	16	11
2	19	11
3	21	11
done	21	11

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
41×	`times-frac`
26×	`sqrt-prod`
24×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--`

Counts

3 → 97

Calls

3 calls:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
17.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
28.0ms	(/ (- 1.0 x) (+ 1.0 x))

series143.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
90.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
49.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify1.3s

Counts

106 → 106

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	173	1505
1	372	1422
2	918	1333
3	2332	1320
done	5000	1300

prune245.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan (sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x)))))
0.0b	(/ (+ 1.0 x) (- 1.0 x))
0.0b	(sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x))))
0.0b	(/ 1 (/ (+ 1.0 x) (- 1.0 x)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

322×	`times-frac`
289×	`*-un-lft-identity`
214×	`add-sqr-sqrt`
139×	`add-cube-cbrt`
83×	`sqrt-prod`
41×	`distribute-lft-out`
33×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-/r*`
18×	`associate-/r/`
17×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`div-inv`
8×	`flip3--` `div-exp` `flip--`
7×	`pow1` `associate-/l*`
5×	`rem-sqrt-square`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1`
2×	`rec-exp` `pow-flip` `frac-2neg` `1-exp` `clear-num` `associate-/l/` `inv-pow`
1×	`flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 288

Calls

4 calls:

1.0ms	(atan (sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x)))))
25.0ms	(/ (+ 1.0 x) (- 1.0 x))
30.0ms	(sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x))))
25.0ms	(/ 1 (/ (+ 1.0 x) (- 1.0 x)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan (sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x)))))
31.0ms	(/ (+ 1.0 x) (- 1.0 x))
88.0ms	(sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x))))
37.0ms	(/ 1 (/ (+ 1.0 x) (- 1.0 x)))

simplify1.9s

Counts

300 → 300

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	376	5529
1	720	4659
2	1590	4160
3	4198	3921
done	5000	3917

prune401.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (/ (+ 1.0 x) (- 1.0 x))))
0.0b	(/ (+ 1.0 x) (- 1.0 x))
0.0b	(atan (fabs (/ 1 (sqrt (/ (+ 1.0 x) (- 1.0 x))))))
0.0b	(sqrt (/ (+ 1.0 x) (- 1.0 x)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

211×	`*-un-lft-identity`
208×	`times-frac`
152×	`add-sqr-sqrt`
130×	`sqrt-prod`
99×	`add-cube-cbrt`
34×	`associate-/r*`
31×	`distribute-lft-out`
25×	`distribute-lft-out--` `difference-of-squares`
13×	`associate-/r/`
10×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`pow1` `div-inv` `associate-/l*`
6×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `div-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `clear-num` `associate-/l/`
1×	`rec-exp` `flip3-+` `1-exp` `flip-+` `inv-pow`

Counts

4 → 236

Calls

4 calls:

26.0ms	(/ 1 (sqrt (/ (+ 1.0 x) (- 1.0 x))))
27.0ms	(/ (+ 1.0 x) (- 1.0 x))
1.0ms	(atan (fabs (/ 1 (sqrt (/ (+ 1.0 x) (- 1.0 x))))))
17.0ms	(sqrt (/ (+ 1.0 x) (- 1.0 x)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ 1 (sqrt (/ (+ 1.0 x) (- 1.0 x))))
36.0ms	(/ (+ 1.0 x) (- 1.0 x))
3.0ms	(atan (fabs (/ 1 (sqrt (/ (+ 1.0 x) (- 1.0 x))))))
87.0ms	(sqrt (/ (+ 1.0 x) (- 1.0 x)))

simplify1.7s

Counts

248 → 248

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	314	4422
1	576	3922
2	1214	3716
3	2870	3653
done	5000	3619

prune447.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (- 1.0 x)))
0.0b	(/ (+ 1.0 x) (sqrt (- 1.0 x)))
0.0b	(* (/ 1 (sqrt (/ 1 (sqrt (- 1.0 x))))) (/ 1 (sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x))))))
0.0b	(/ 1 (sqrt (/ 1 (sqrt (- 1.0 x)))))

rewrite416.0ms

Algorithm

rewrite-expression-head

Rules

977×	`times-frac`
828×	`add-sqr-sqrt`
764×	`sqrt-prod`
608×	`*-un-lft-identity`
316×	`add-cube-cbrt`
128×	`associate-r`
117×	`unswap-sqr`
104×	`associate-l`
54×	`add-exp-log`
49×	`associate-/r*`
42×	`distribute-lft-out--` `difference-of-squares`
33×	`distribute-lft-out`
27×	`sqrt-div` `associate-/r/`
22×	`add-cbrt-cube`
21×	`div-exp`
19×	`pow-flip`
16×	`pow1` `prod-exp`
15×	`div-inv`
12×	`flip3--` `flip--`
10×	`rec-exp` `1-exp` `associate-/l*`
9×	`sqrt-pow1`
7×	`cbrt-undiv`
5×	`pow1/2` `pow-prod-down` `inv-pow`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/l/`
1×	`frac-times` `flip3-+` `associate-r/` `associate-l/` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 667

Calls

4 calls:

14.0ms	(/ 1 (sqrt (- 1.0 x)))
27.0ms	(/ (+ 1.0 x) (sqrt (- 1.0 x)))
283.0ms	(* (/ 1 (sqrt (/ 1 (sqrt (- 1.0 x))))) (/ 1 (sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x))))))
28.0ms	(/ 1 (sqrt (/ 1 (sqrt (- 1.0 x)))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ 1 (sqrt (- 1.0 x)))
87.0ms	(/ (+ 1.0 x) (sqrt (- 1.0 x)))
88.0ms	(* (/ 1 (sqrt (/ 1 (sqrt (- 1.0 x))))) (/ 1 (sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x))))))
92.0ms	(/ 1 (sqrt (/ 1 (sqrt (- 1.0 x)))))

simplify1.7s

Counts

679 → 679

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	742	17247
1	1891	14713
2	3526	13801
done	5001	13772

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes22.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	15	13
done	15	13

end0.0ms

sample745.0ms

Algorithm

intervals

Results

300.0ms	8000×	body	80	valid
195.0ms	7910×	body	80	nan