Details

sample335.0ms

Algorithm

intervals

Results

108.0ms	289×	body	80	nan
76.0ms	44×	body	10240	exit
51.0ms	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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

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

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:

22.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
14.0ms	(pow (sqrt (atan2 b b)) (- b a))
6.0ms	(sqrt (atan2 b b))

series153.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
32.0ms	(pow (sqrt (atan2 b b)) (- b a))
30.0ms	(sqrt (atan2 b b))

simplify2.4s

Counts

60 → 60

Iterations

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

prune342.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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)))

rewrite37.0ms

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×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
1×	`pow-to-exp` `pow-pow` `div-sub` `pow-exp` `div-inv` `pow-sub` `sqr-pow`

Counts

2 → 43

Calls

2 calls:

16.0ms	(pow (atan2 b b) (/ (- b a) 2))
19.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))

series133.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(pow (atan2 b b) (/ (- b a) 2))
97.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))

simplify1.7s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
3	2090
2	658
1	254
0	102

prune275.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize46.0ms

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))))

rewrite535.0ms

Algorithm

rewrite-expression-head

Rules

1088×	`times-frac`
862×	`*-un-lft-identity`
640×	`pow-unpow`
626×	`add-sqr-sqrt`
470×	`add-cube-cbrt`
136×	`distribute-lft-out--`
108×	`pow-prod-down`
84×	`pow-prod-up`
82×	`pow-sqr`
72×	`difference-of-squares`
32×	`div-inv`
24×	`unpow-prod-down`
21×	`pow1`
18×	`add-exp-log`
12×	`div-sub` `sqr-pow`
10×	`pow-pow`
9×	`prod-exp` `unswap-sqr`
8×	`pow-to-exp` `pow-exp`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`add-cbrt-cube` `pow-sub`
4×	`insert-posit16` `add-log-exp`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 490

Calls

4 calls:

13.0ms	(pow (atan2 b b) (/ (/ (- b a) 2) 2))
20.0ms	(pow (atan2 b b) (/ (/ (- b a) 2) 2))
339.0ms	(* (pow (atan2 b b) (/ (/ (- b a) 2) 2)) (pow (atan2 b b) (/ (/ (- b a) 2) 2)))
90.0ms	(sin (* (pow (atan2 b b) (/ (/ (- b a) 2) 2)) (pow (atan2 b b) (/ (/ (- b a) 2) 2))))

series183.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (atan2 b b) (/ (/ (- b a) 2) 2))
29.0ms	(pow (atan2 b b) (/ (/ (- b a) 2) 2))
34.0ms	(* (pow (atan2 b b) (/ (/ (- b a) 2) 2)) (pow (atan2 b b) (/ (/ (- b a) 2) 2)))
97.0ms	(sin (* (pow (atan2 b b) (/ (/ (- b a) 2) 2)) (pow (atan2 b b) (/ (/ (- b a) 2) 2))))

simplify3.4s

Counts

502 → 502

Iterations

Iter	Nodes
done	5001
2	4166
1	1229
0	462

prune2.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize29.0ms

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)))

rewrite186.0ms

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))))
150.0ms	(* (* (- b a) (log (sqrt (atan2 b b)))) (cos 1))
2.0ms	(sqrt (atan2 b b))
5.0ms	(log (sqrt (atan2 b b)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (- b a) (log (sqrt (atan2 b b))))
236.0ms	(* (* (- b a) (log (sqrt (atan2 b b)))) (cos 1))
12.0ms	(sqrt (atan2 b b))
73.0ms	(log (sqrt (atan2 b b)))

simplify3.1s

Counts

121 → 121

Iterations

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

prune554.0ms

Pruning

2 alts after pruning (0 fresh and 2 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

simplify3.0ms

Iterations

Iter	Nodes
done	10
0	10

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.5s	9747×	body	80	nan
2.2s	1767×	body	10240	exit
1.5s	7993×	body	80	valid
4.0ms	2×	body	2560	valid
4.0ms	4×	body	640	valid
0.0ms	1×	body	160	valid