Details

sample277.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
7.0ms	272×	body	80	nan

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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))

rewrite29.0ms

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:

0.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
10.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
14.0ms	(/ (- 1.0 x) (+ 1.0 x))

series151.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
96.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
52.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify1.2s

Counts

106 → 106

Iterations

Useful iterations: 3 (559.0ms)

Iter	Nodes	Cost
0	173	1505
1	368	1422
2	901	1373
3	2446	1320
done	5000	1320

prune242.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(/ (- 1.0 x) (+ 1.0 x))
0.0b	(cbrt (pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3))
0.0b	(pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

183×	`*-un-lft-identity`
130×	`sqrt-prod`
124×	`add-sqr-sqrt`
121×	`times-frac`
71×	`add-cube-cbrt`
64×	`cbrt-prod`
58×	`unpow-prod-down` `cube-prod`
31×	`distribute-lft-out`
25×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r/`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`flip3-+` `flip-+` `div-inv`
5×	`associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-pow` `sqrt-div`
2×	`cube-div` `cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `flip3--` `frac-2neg` `pow1/3` `div-sub` `div-exp` `pow-exp` `clear-num` `sqrt-pow2` `flip--` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 245

Calls

4 calls:

10.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
12.0ms	(/ (- 1.0 x) (+ 1.0 x))
19.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3))
14.0ms	(pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3)

series415.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
38.0ms	(/ (- 1.0 x) (+ 1.0 x))
92.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3))
192.0ms	(pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3)

simplify733.0ms

Counts

257 → 257

Iterations

Useful iterations: 2 (308.0ms)

Iter	Nodes	Cost
0	283	4876
1	707	4008
2	1673	3841
done	5000	3841

prune501.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(/ (- 1.0 x) (+ 1.0 x))
0.0b	(log1p (expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
0.0b	(expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

10.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
12.0ms	(/ (- 1.0 x) (+ 1.0 x))
0.0ms	(log1p (expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
1.0ms	(expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
33.0ms	(/ (- 1.0 x) (+ 1.0 x))
117.0ms	(log1p (expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
45.0ms	(expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))

simplify1.2s

Counts

122 → 122

Iterations

Useful iterations: 3 (586.0ms)

Iter	Nodes	Cost
0	187	1719
1	386	1604
2	945	1517
3	2530	1480
done	5000	1480

prune304.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes57.0ms

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	12	14
1	14	14
done	14	14

end0.0ms

sample699.0ms

Algorithm

intervals

Results

312.0ms	8000×	body	80	valid
200.0ms	8067×	body	80	nan