Details

sample216.0ms

Algorithm

intervals

Results

51.0ms	44×	body	10240	exit
35.0ms	289×	body	80	nan
35.0ms	256×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	1114
5	256
4	110
3	45
2	22
1	13
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

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))

rewrite46.0ms

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:

27.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
11.0ms	(pow (sqrt (atan2 b b)) (- b a))
4.0ms	(sqrt (atan2 b b))

series193.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
40.0ms	(pow (sqrt (atan2 b b)) (- b a))
33.0ms	(sqrt (atan2 b b))

simplify2.1s

Counts

75 → 75

Iterations

Iter	Nodes
done	5006
3	1724
2	687
1	311
0	120

prune304.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

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:

10.0ms	(pow (atan2 b b) (/ (- b a) 2))
14.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))

series143.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(pow (atan2 b b) (/ (- b a) 2))
110.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))

simplify2.8s

Counts

53 → 53

Iterations

Iter	Nodes
done	5002
3	2134
2	688
1	260
0	106

prune293.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
156×	`add-sqr-sqrt`
144×	`*-un-lft-identity`
122×	`pow-unpow`
108×	`add-cube-cbrt`
24×	`unpow-prod-down`
18×	`add-exp-log` `distribute-lft-out--` `difference-of-squares`
12×	`div-sub` `sqr-pow`
9×	`prod-exp` `unswap-sqr`
8×	`pow-to-exp` `pow-exp` `div-inv`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`pow1` `add-cbrt-cube` `pow-sub`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-pow`
1×	`pow2` `frac-times` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 226

Calls

4 calls:

8.0ms	(pow (atan2 b b) (/ (/ (- b a) 2) 2))
6.0ms	(pow (atan2 b b) (/ (/ (- b a) 2) 2))
27.0ms	(* (pow (atan2 b b) (/ (/ (- b a) 2) 2)) (pow (atan2 b b) (/ (/ (- b a) 2) 2)))
70.0ms	(sin (* (pow (atan2 b b) (/ (/ (- b a) 2) 2)) (pow (atan2 b b) (/ (/ (- b a) 2) 2))))

series244.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(pow (atan2 b b) (/ (/ (- b a) 2) 2))
32.0ms	(pow (atan2 b b) (/ (/ (- b a) 2) 2))
35.0ms	(* (pow (atan2 b b) (/ (/ (- b a) 2) 2)) (pow (atan2 b b) (/ (/ (- b a) 2) 2)))
136.0ms	(sin (* (pow (atan2 b b) (/ (/ (- b a) 2) 2)) (pow (atan2 b b) (/ (/ (- b a) 2) 2))))

simplify2.3s

Counts

238 → 238

Iterations

Iter	Nodes
done	5002
2	2098
1	738
0	247

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (log (sqrt (atan2 b b))) (* (cos 1) (- b a)) (sin 1))
0.6b	(* (cos 1) (- b a))
1.0b	(sqrt (atan2 b b))
2.0b	(log (sqrt (atan2 b b)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
7×	`add-exp-log`
6×	`log-prod` `add-cbrt-cube` `sqrt-prod`
5×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `log-pow`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`rem-sqrt-square` `flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

0.0ms	(fma (log (sqrt (atan2 b b))) (* (cos 1) (- b a)) (sin 1))
19.0ms	(* (cos 1) (- b a))
1.0ms	(sqrt (atan2 b b))
2.0ms	(log (sqrt (atan2 b b)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(fma (log (sqrt (atan2 b b))) (* (cos 1) (- b a)) (sin 1))
200.0ms	(* (cos 1) (- b a))
19.0ms	(sqrt (atan2 b b))
93.0ms	(log (sqrt (atan2 b b)))

simplify2.4s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
3	1959
2	726
1	313
0	158

prune461.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes78.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	10
0	10

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.3s	1767×	body	10240	exit
2.1s	9747×	body	80	nan
1.9s	7993×	body	80	valid
4.0ms	4×	body	640	valid
3.0ms	2×	body	2560	valid
0.0ms	1×	body	160	valid