Details

sample415.0ms

Algorithm

intervals

Results

46.0ms	54×	body	10240	exit
16.0ms	365×	body	80	nan
16.0ms	256×	body	80	valid

simplify57.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 0.1b

localize11.0ms

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))

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:

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

series115.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
25.0ms	(pow (sqrt (atan2 b b)) (- b a))
18.0ms	(sqrt (atan2 b b))

simplify46.0ms

Counts

57 → 57

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	148	324
1	412	298
2	1345	292
3	5001	290
done	5001	290

prune129.0ms

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

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

series87.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
22.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

simplify58.0ms

Counts

32 → 32

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	145	236
1	453	212
2	1900	202
3	5001	199
done	5001	199

prune69.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

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))

rewrite60.0ms

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` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 162

Calls

4 calls:

8.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
42.0ms	(* (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))

series99.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
43.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
11.0ms	(sqrt (atan2 b b))
14.0ms	(sqrt (atan2 b b))

simplify54.0ms

Counts

174 → 174

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	292	1754
1	1319	1646
2	5002	1602
done	5002	1602

prune345.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (log (pow (exp 1) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
0.0b	(log (pow (exp 1) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
0.0b	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

15×	`unpow-prod-down`
14×	`log-prod`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
8×	`pow1`
7×	`sin-sum`
6×	`add-exp-log`
5×	`pow-pow` `sqrt-pow1`
4×	`unpow-prod-up` `add-cbrt-cube` `add-log-exp`
3×	`pow1/2` `rem-log-exp` `sqr-pow`
2×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `distribute-lft-in` `pow-exp`
1×	`rem-sqrt-square` `pow-unpow` `log-pow` `sqrt-pow2`

Counts

4 → 75

Calls

4 calls:

10.0ms	(sin (log (pow (exp 1) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
4.0ms	(log (pow (exp 1) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
9.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0ms	(sqrt (atan2 b b))

series242.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sin (log (pow (exp 1) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
77.0ms	(log (pow (exp 1) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
34.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
11.0ms	(sqrt (atan2 b b))

simplify43.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	314	1056
1	990	944
2	5002	906
done	5002	906

prune261.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes39.0ms

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

774.0ms	1809×	body	10240	exit
448.0ms	10114×	body	80	nan
438.0ms	7989×	body	80	valid
9.0ms	3×	body	5120	valid
1.0ms	1×	body	2560	valid
1.0ms	2×	body	1280	valid
0.0ms	2×	body	320	valid
0.0ms	1×	body	640	valid
0.0ms	2×	body	160	valid