Details

sample260.0ms

Algorithm

intervals

Results

47.0ms	51×	body	10240	exit
33.0ms	256×	body	80	valid
32.0ms	300×	body	80	nan

simplify1.7s

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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))

rewrite23.0ms

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	(sin (pow (sqrt (atan2 b b)) (- b a)))
5.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series142.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
25.0ms	(pow (sqrt (atan2 b b)) (- b a))
18.0ms	(sqrt (atan2 b b))

simplify2.5s

Counts

60 → 60

Iterations

Iter	Nodes
done	5032
4	3465
3	1051
2	391
1	184
0	78

prune300.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
20×	`add-sqr-sqrt`
18×	`unpow-prod-down` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`pow1/2` `add-exp-log`
4×	`unpow-prod-up` `add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

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

series117.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
40.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
19.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))

simplify3.8s

Counts

108 → 108

Iterations

Iter	Nodes
done	5002
4	3943
3	1208
2	490
1	214
0	84

prune568.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

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)))

rewrite21.0ms

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:

17.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
4.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

series108.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
24.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

simplify1.9s

Counts

34 → 34

Iterations

Iter	Nodes
done	5001
3	1473
2	425
1	159
0	68

prune203.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (pow (atan2 b b) (* 1/2 (- b a)))) (cbrt (pow (atan2 b b) (* 1/2 (- b a)))))
0.3b	(cbrt (pow (atan2 b b) (* 1/2 (- b a))))
0.3b	(cbrt (pow (atan2 b b) (* 1/2 (- b a))))
0.3b	(cbrt (pow (atan2 b b) (* 1/2 (- b a))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

109×	`cbrt-prod`
46×	`add-sqr-sqrt`
36×	`unpow-prod-up`
29×	`unpow-prod-down`
22×	`*-un-lft-identity` `add-cube-cbrt`
18×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `swap-sqr`
16×	`unswap-sqr`
15×	`sqr-pow`
14×	`associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 141

Calls

4 calls:

36.0ms	(* (cbrt (pow (atan2 b b) (* 1/2 (- b a)))) (cbrt (pow (atan2 b b) (* 1/2 (- b a)))))
3.0ms	(cbrt (pow (atan2 b b) (* 1/2 (- b a))))
7.0ms	(cbrt (pow (atan2 b b) (* 1/2 (- b a))))
3.0ms	(cbrt (pow (atan2 b b) (* 1/2 (- b a))))

series279.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (cbrt (pow (atan2 b b) (* 1/2 (- b a)))) (cbrt (pow (atan2 b b) (* 1/2 (- b a)))))
72.0ms	(cbrt (pow (atan2 b b) (* 1/2 (- b a))))
44.0ms	(cbrt (pow (atan2 b b) (* 1/2 (- b a))))
58.0ms	(cbrt (pow (atan2 b b) (* 1/2 (- b a))))

simplify1.9s

Counts

153 → 153

Iterations

Iter	Nodes
done	5000
3	1648
2	631
1	260
0	128

prune940.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes101.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
0	9

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.4s	1881×	body	10240	exit
1.6s	9841×	body	80	nan
1.0s	7992×	body	80	valid
5.0ms	1×	body	5120	valid
2.0ms	2×	body	1280	valid
1.0ms	2×	body	320	valid
1.0ms	2×	body	160	valid
0.0ms	1×	body	640	valid