Details

sample155.0ms

Algorithm

intervals

Results

65.0ms	55×	body	10240	exit
35.0ms	256×	body	80	valid
35.0ms	262×	body	80	nan

simplify913.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2044
6	1161
5	250
4	110
3	45
2	22
1	13
0	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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))

rewrite26.0ms

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:

15.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
9.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series125.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
35.0ms	(pow (sqrt (atan2 b b)) (- b a))
25.0ms	(sqrt (atan2 b b))

simplify640.0ms

Counts

60 → 60

Iterations

Iter	Nodes
done	2004
3	1051
2	391
1	184
0	78

prune252.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(sin (pow (atan2 b b) (* 1/2 (- b a))))
0.0b	(pow (atan2 b b) (* 1/2 (- b a)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

4×	`unpow-prod-up`
3×	`add-sqr-sqrt` `pow1` `unpow-prod-down` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-cbrt-cube` `insert-posit16` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 28

Calls

2 calls:

20.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
7.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

series107.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
23.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

simplify649.0ms

Counts

34 → 34

Iterations

Iter	Nodes
done	2001
3	1473
2	425
1	159
0	68

prune139.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

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))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-prod`
87×	`unpow-prod-down`
82×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`unswap-sqr`
23×	`swap-sqr`
17×	`add-exp-log`
15×	`associate-r` `associate-l` `sqr-pow`
14×	`unpow-prod-up`
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×	`pow1/2` `insert-posit16` `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 → 166

Calls

4 calls:

11.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
30.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series152.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
67.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
19.0ms	(sqrt (atan2 b b))
20.0ms	(sqrt (atan2 b b))

simplify912.0ms

Counts

178 → 178

Iterations

Iter	Nodes
done	2001
2	1104
1	396
0	150

prune698.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize54.0ms

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)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
66×	`sqrt-prod`
60×	`unpow-prod-down`
55×	`log-prod`
40×	`exp-sum`
30×	`unswap-sqr`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`associate-r`
15×	`associate-l`
14×	`sqr-pow`
8×	`add-exp-log`
6×	`pow1` `unpow-prod-up` `add-cbrt-cube`
5×	`pow-sub`
4×	`insert-posit16` `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 → 135

Calls

4 calls:

45.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
9.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
15.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
107.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify795.0ms

Counts

147 → 147

Iterations

Iter	Nodes
done	2000
2	944
1	335
0	164

prune736.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes66.0ms

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	12
1	12
0	11

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.9s	1811×	body	10240	exit
2.1s	9580×	body	80	nan
1.4s	7995×	body	80	valid
5.0ms	1×	body	5120	valid
3.0ms	1×	body	2560	valid
1.0ms	2×	body	640	valid
0.0ms	1×	body	160	valid