Details

sample285.0ms

Algorithm

intervals

Results

66.0ms	59×	body	10240	exit
38.0ms	327×	body	80	nan
37.0ms	255×	body	80	valid
0.0ms	1×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5019
6	1161
5	250
4	110
3	45
2	22
1	13
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
0.2b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`pow-pow` `add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`unpow-prod-up` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 51

Calls

3 calls:

13.0ms	(pow (sqrt (atan2 b b)) (- b a))
9.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms	(sqrt (atan2 b b))

series174.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(pow (sqrt (atan2 b b)) (- b a))
111.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
31.0ms	(sqrt (atan2 b b))

simplify2.6s

Counts

60 → 60

Iterations

Iter	Nodes
done	5007
4	3718
3	1092
2	392
1	184
0	78

prune260.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
0.2b	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-prod`
78×	`unpow-prod-down`
76×	`add-sqr-sqrt`
25×	`unswap-sqr`
23×	`swap-sqr`
22×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-exp-log`
15×	`associate-r` `associate-l`
14×	`sqr-pow`
12×	`unpow-prod-up`
9×	`prod-exp`
6×	`pow-to-exp` `pow1` `sub-neg` `add-cbrt-cube` `pow-exp`
4×	`insert-posit16` `pow-sub` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 140

Calls

4 calls:

51.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
61.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series212.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
116.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
19.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))

simplify3.0s

Counts

152 → 152

Iterations

Iter	Nodes
done	5001
3	3171
2	930
1	318
0	149

prune575.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (cbrt (atan2 b b))) (- b a))
0.2b	(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (sqrt (cbrt (atan2 b b))) (- b a))))
1.0b	(cbrt (atan2 b b))
1.0b	(cbrt (atan2 b b))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`cbrt-prod` `unpow-prod-down`
6×	`pow1` `sqrt-prod`
5×	`pow-unpow` `add-exp-log`
4×	`pow-pow` `add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`pow1/3`
2×	`unpow-prod-up` `sqrt-pow1`
1×	`pow-to-exp` `sub-neg` `pow1/2` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 65

Calls

4 calls:

8.0ms	(pow (sqrt (cbrt (atan2 b b))) (- b a))
49.0ms	(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (sqrt (cbrt (atan2 b b))) (- b a))))
2.0ms	(cbrt (atan2 b b))
2.0ms	(cbrt (atan2 b b))

series560.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (sqrt (cbrt (atan2 b b))) (- b a))
214.0ms	(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (sqrt (cbrt (atan2 b b))) (- b a))))
143.0ms	(cbrt (atan2 b b))
168.0ms	(cbrt (atan2 b b))

simplify1.7s

Counts

77 → 77

Iterations

Iter	Nodes
done	5003
3	1671
2	653
1	274
0	112

prune508.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (fabs (cbrt (atan2 b b))) (- b a))
0.2b	(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (cbrt (atan2 b b)) (/ (- b a) 2))))
1.0b	(cbrt (atan2 b b))
1.0b	(cbrt (atan2 b b))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
6×	`cbrt-prod`
5×	`pow1` `pow-unpow` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`unpow-prod-down`
2×	`unpow-prod-up` `pow1/3`
1×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

11.0ms	(pow (fabs (cbrt (atan2 b b))) (- b a))
53.0ms	(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (cbrt (atan2 b b)) (/ (- b a) 2))))
1.0ms	(cbrt (atan2 b b))
1.0ms	(cbrt (atan2 b b))

series594.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (fabs (cbrt (atan2 b b))) (- b a))
223.0ms	(sin (* (pow (fabs (cbrt (atan2 b b))) (- b a)) (pow (cbrt (atan2 b b)) (/ (- b a) 2))))
191.0ms	(cbrt (atan2 b b))
150.0ms	(cbrt (atan2 b b))

simplify1.7s

Counts

67 → 67

Iterations

Iter	Nodes
done	5002
3	1859
2	578
1	227
0	98

prune392.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes98.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	13
1	13
0	12

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.1s	1797×	body	10240	exit
1.4s	7991×	body	80	valid
1.2s	9799×	body	80	nan
11.0ms	4×	body	2560	valid
3.0ms	1×	body	5120	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	640	valid