Details

sample148.0ms

Algorithm

intervals

Results

62.0ms	55×	body	10240	exit
35.0ms	262×	body	80	nan
34.0ms	256×	body	80	valid

simplify953.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2040
6	1114
5	256
4	110
3	45
2	22
1	13
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`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 → 66

Calls

3 calls:

8.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
5.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series125.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
33.0ms	(pow (sqrt (atan2 b b)) (- b a))
18.0ms	(sqrt (atan2 b b))

simplify1.0s

Counts

75 → 75

Iterations

Iter	Nodes
done	2001
3	1724
2	687
1	311
0	120

prune301.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(sin (pow (atan2 b b) (/ (- b a) 2)))
0.0b	(pow (atan2 b b) (/ (- b a) 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow-unpow`
18×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
3×	`pow1` `unpow-prod-down` `add-exp-log` `distribute-lft-out--` `difference-of-squares`
2×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `pow-pow` `div-sub` `pow-exp` `div-inv` `pow-sub` `sqr-pow`

Counts

2 → 47

Calls

2 calls:

15.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))
10.0ms	(pow (atan2 b b) (/ (- b a) 2))

series130.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))
37.0ms	(pow (atan2 b b) (/ (- b a) 2))

simplify569.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	2003
2	693
1	260
0	106

prune264.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.0b	(* (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))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
93×	`sqrt-prod`
87×	`unpow-prod-down`
59×	`unpow-prod-up`
58×	`*-un-lft-identity`
56×	`add-cube-cbrt`
45×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
17×	`add-exp-log`
15×	`sqr-pow`
9×	`pow1` `prod-exp`
7×	`pow-to-exp` `sub-neg` `pow-exp`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow` `pow-sub`
4×	`expm1-log1p-u` `pow1/2` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `sqrt-pow2` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 210

Calls

4 calls:

6.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
28.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
5.0ms	(sqrt (atan2 b b))

series131.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
51.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
19.0ms	(sqrt (atan2 b b))
21.0ms	(sqrt (atan2 b b))

simplify1.2s

Counts

222 → 222

Iterations

Iter	Nodes
done	2000
2	1791
1	582
0	216

prune876.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
3.3b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
73×	`log-prod`
66×	`sqrt-prod`
60×	`unpow-prod-down`
49×	`exp-sum`
37×	`*-un-lft-identity` `add-cube-cbrt`
33×	`unpow-prod-up`
30×	`unswap-sqr`
27×	`associate-r` `prod-diff`
24×	`associate-l`
14×	`sqr-pow`
8×	`add-exp-log`
6×	`pow1` `add-cbrt-cube`
5×	`pow-sub`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-div` `sub-neg` `rem-log-exp` `prod-exp`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `exp-diff` `pow-exp`
1×	`frac-times` `associate-l/` `associate-r/` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 170

Calls

4 calls:

75.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
5.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series175.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
11.0ms	(sqrt (atan2 b b))
21.0ms	(sqrt (atan2 b b))
87.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify822.0ms

Counts

182 → 182

Iterations

Iter	Nodes
done	2002
2	1168
1	506
0	241

prune1.0s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes56.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.8s	1811×	body	10240	exit
1.7s	9580×	body	80	nan
1.7s	7995×	body	80	valid
5.0ms	1×	body	5120	valid
2.0ms	2×	body	640	valid
1.0ms	1×	body	2560	valid
0.0ms	1×	body	160	valid