Details

sample126.0ms

Algorithm

intervals

Results

44.0ms	47×	body	10240	exit
28.0ms	293×	body	80	nan
26.0ms	255×	body	80	valid
5.0ms	1×	body	5120	valid

simplify661.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	438
4	117
3	45
2	22
1	13
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
0.3b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite27.0ms

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` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 48

Calls

3 calls:

11.0ms	(pow (sqrt (atan2 b b)) (- b a))
11.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms	(sqrt (atan2 b b))

series155.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(pow (sqrt (atan2 b b)) (- b a))
90.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
23.0ms	(sqrt (atan2 b b))

simplify2.0s

Counts

57 → 57

Iterations

Iter	Nodes
done	5002
3	4131
2	653
1	188
0	75

prune298.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

13.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
42.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series238.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
163.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
20.0ms	(sqrt (atan2 b b))
20.0ms	(sqrt (atan2 b b))

simplify388.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	944
1	265
0	104

prune494.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (* (- b a) (log (sqrt (sqrt (atan2 b b))))))))
0.3b	(* (- b a) (log (sqrt (sqrt (atan2 b b)))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
20×	`add-sqr-sqrt`
18×	`log-prod`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`distribute-rgt-in` `distribute-lft-in`
8×	`associate-r`
6×	`sqrt-pow1` `add-cbrt-cube` `add-exp-log`
5×	`associate-l` `log-pow`
4×	`pow1/2` `add-log-exp`
2×	`rem-sqrt-square` `associate-*l/`
1×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

27.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (* (- b a) (log (sqrt (sqrt (atan2 b b))))))))
41.0ms	(* (- b a) (log (sqrt (sqrt (atan2 b b)))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series402.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (* (- b a) (log (sqrt (sqrt (atan2 b b))))))))
203.0ms	(* (- b a) (log (sqrt (sqrt (atan2 b b)))))
22.0ms	(sqrt (atan2 b b))
17.0ms	(sqrt (atan2 b b))

simplify610.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1087
1	283
0	140

prune522.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
0.3b	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
0.3b	(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0b	(sqrt (atan2 b b))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`log-prod`
5×	`add-exp-log`
4×	`exp-prod` `add-cbrt-cube` `add-log-exp`
3×	`exp-sum` `sqrt-prod`
2×	`log-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `rem-exp-log`

Counts

4 → 47

Calls

4 calls:

11.0ms	(exp (log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
13.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
10.0ms	(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0ms	(sqrt (atan2 b b))

series422.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(exp (log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
129.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
184.0ms	(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
14.0ms	(sqrt (atan2 b b))

simplify671.0ms

Counts

59 → 59

Iterations

Iter	Nodes
done	5001
3	1375
2	371
1	150
0	80

prune403.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes118.0ms

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	14
1	14
0	12

end0.0ms

sample5.4s

Algorithm

intervals

Results

1.7s	1888×	body	10240	exit
1.6s	7988×	body	80	valid
1.4s	9645×	body	80	nan
25.0ms	5×	body	5120	valid
2.0ms	6×	body	160	valid
1.0ms	1×	body	320	valid