Details

sample206.0ms

Algorithm

intervals

Results

75.0ms	289×	body	80	nan
63.0ms	44×	body	10240	exit
44.0ms	256×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

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))

rewrite25.0ms

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:

12.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
11.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series156.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
36.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(sqrt (atan2 b b))

simplify2.3s

Counts

60 → 60

Iterations

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

prune368.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

16.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
24.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

series114.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
80.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify1.8s

Counts

47 → 47

Iterations

Iter	Nodes
done	5007
3	2232
2	672
1	261
0	96

prune283.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite476.0ms

Algorithm

rewrite-expression-head

Rules

478×	`pow-unpow`
440×	`times-frac`
416×	`*-un-lft-identity`
346×	`add-sqr-sqrt`
238×	`add-cube-cbrt`
175×	`associate-r`
101×	`associate-l`
83×	`pow-prod-down`
63×	`pow-prod-up`
61×	`pow-sqr`
48×	`distribute-lft-out--`
33×	`unswap-sqr`
25×	`*-commutative`
24×	`unpow-prod-down` `difference-of-squares`
21×	`pow1`
18×	`add-exp-log`
12×	`sqr-pow`
10×	`pow-pow`
9×	`prod-exp`
8×	`pow-to-exp` `pow-exp` `div-inv`
7×	`swap-sqr`
6×	`add-cbrt-cube`
4×	`insert-posit16` `add-log-exp`
1×	`pow2` `pow-plus` `cbrt-unprod`

Counts

4 → 388

Calls

4 calls:

17.0ms	(pow (atan2 b b) (/ (* 1/2 (- b a)) 2))
26.0ms	(pow (atan2 b b) (/ (* 1/2 (- b a)) 2))
57.0ms	(sin (* (pow (atan2 b b) (/ (* 1/2 (- b a)) 2)) (pow (atan2 b b) (/ (* 1/2 (- b a)) 2))))
324.0ms	(* (pow (atan2 b b) (/ (* 1/2 (- b a)) 2)) (pow (atan2 b b) (/ (* 1/2 (- b a)) 2)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (atan2 b b) (/ (* 1/2 (- b a)) 2))
28.0ms	(pow (atan2 b b) (/ (* 1/2 (- b a)) 2))
128.0ms	(sin (* (pow (atan2 b b) (/ (* 1/2 (- b a)) 2)) (pow (atan2 b b) (/ (* 1/2 (- b a)) 2))))
41.0ms	(* (pow (atan2 b b) (/ (* 1/2 (- b a)) 2)) (pow (atan2 b b) (/ (* 1/2 (- b a)) 2)))

simplify2.5s

Counts

400 → 400

Iterations

Iter	Nodes
done	5000
2	3185
1	977
0	366

prune2.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
27×	`associate-l`
21×	`*-un-lft-identity`
18×	`pow1` `log-prod`
17×	`add-cube-cbrt`
15×	`associate-r`
12×	`add-exp-log` `sqrt-prod`
11×	`add-cbrt-cube`
9×	`log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`
5×	`unswap-sqr`
4×	`sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`*-commutative`
2×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 109

Calls

4 calls:

26.0ms	(* (- b a) (log (sqrt (atan2 b b))))
134.0ms	(* (* (- b a) (log (sqrt (atan2 b b)))) (cos 1))
2.0ms	(sqrt (atan2 b b))
2.0ms	(log (sqrt (atan2 b b)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (- b a) (log (sqrt (atan2 b b))))
246.0ms	(* (* (- b a) (log (sqrt (atan2 b b)))) (cos 1))
19.0ms	(sqrt (atan2 b b))
115.0ms	(log (sqrt (atan2 b b)))

simplify3.0s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
3	3810
2	884
1	291
0	136

prune545.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes54.0ms

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

2.6s	9747×	body	80	nan
2.3s	1767×	body	10240	exit
1.4s	7993×	body	80	valid
6.0ms	2×	body	2560	valid
3.0ms	4×	body	640	valid
0.0ms	1×	body	160	valid