Details

sample395.0ms

Algorithm

intervals

Results

49.0ms	61×	body	10240	exit
16.0ms	348×	body	80	nan
16.0ms	256×	body	80	valid

simplify60.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	5
1	22	5
2	44	5
3	114	5
4	315	5
5	1609	5
6	5001	5
done	5001	5

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite21.0ms

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` `add-log-exp`
2×	`unpow-prod-up` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 48

Calls

3 calls:

6.0ms	(pow (sqrt (atan2 b b)) (- b a))
9.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms	(sqrt (atan2 b b))

series114.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(pow (sqrt (atan2 b b)) (- b a))
73.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
18.0ms	(sqrt (atan2 b b))

simplify47.0ms

Counts

57 → 57

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	148	324
1	412	298
2	1346	292
3	5001	290
done	5001	290

prune125.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

4.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
11.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

series85.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
63.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify57.0ms

Counts

32 → 32

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	145	236
1	453	212
2	1901	202
3	5001	199
done	5001	199

prune66.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (pow (atan2 b b) (* 1/2 (- b a))))
0.0b	(* (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))) (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))))
0.2b	(sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))
0.2b	(sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

11.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
47.0ms	(* (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))) (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))))
8.0ms	(sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))
8.0ms	(sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
65.0ms	(* (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))) (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))))
106.0ms	(sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))
107.0ms	(sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))

simplify175.0ms

Counts

94 → 94

Iterations

Useful iterations: 3 (167.0ms)

Iter	Nodes	Cost
0	166	828
1	650	734
2	3877	678
3	5003	655
done	5003	655

prune188.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))))
0.2b	(cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))))
0.3b	(* (* (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))) (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))))) (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))))
0.3b	(* (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))) (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-prod`
48×	`add-sqr-sqrt`
30×	`pow1` `sqrt-prod`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`associate-r`
17×	`pow1/3`
12×	`unswap-sqr`
11×	`add-exp-log` `swap-sqr` `pow-prod-up`
10×	`associate-l`
7×	`pow-plus` `pow-prod-down`
5×	`pow-sqr` `add-cbrt-cube`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`pow2`
2×	`*-commutative`
1×	`pow3`

Counts

4 → 123

Calls

4 calls:

6.0ms	(cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))))
6.0ms	(cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))))
98.0ms	(* (* (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))) (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))))) (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))))
50.0ms	(* (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))) (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))))

series512.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))))
133.0ms	(cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))))
107.0ms	(* (* (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))) (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a))))))) (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))))
136.0ms	(* (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))) (cbrt (sqrt (sin (pow (atan2 b b) (* 1/2 (- b a)))))))

simplify57.0ms

Counts

135 → 135

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	303	2338
1	1275	2040
2	5002	1777
done	5002	1777

prune313.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	5
1	9	5
done	9	5

end0.0ms

sample2.2s

Algorithm

intervals

Results

808.0ms	1848×	body	10240	exit
453.0ms	7991×	body	80	valid
450.0ms	9800×	body	80	nan
3.0ms	1×	body	5120	valid
2.0ms	2×	body	2560	valid
2.0ms	3×	body	1280	valid
1.0ms	2×	body	640	valid
0.0ms	1×	body	320	valid