Details

sample126.0ms

Algorithm

intervals

Results

41.0ms	47×	body	10240	exit
27.0ms	294×	body	80	nan
26.0ms	256×	body	80	valid

simplify682.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	444
4	117
3	45
2	22
1	13
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`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 → 63

Calls

3 calls:

10.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
8.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series152.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
38.0ms	(pow (sqrt (atan2 b b)) (- b a))
22.0ms	(sqrt (atan2 b b))

simplify710.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1098
1	315
0	117

prune266.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

22×	`unpow-prod-up`
18×	`prod-diff`
15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
3×	`pow1` `unpow-prod-down` `add-exp-log`
2×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 48

Calls

2 calls:

12.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
32.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

series110.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
73.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify698.0ms

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
2	1240
1	359
0	144

prune249.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (atan2 b b) (- b a))
0.0b	(sin (log (exp (sqrt (pow (atan2 b b) (- b a))))))
0.0b	(exp (sqrt (pow (atan2 b b) (- b a))))
0.0b	(log (exp (sqrt (pow (atan2 b b) (- b a)))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

42×	`exp-prod`
36×	`sqrt-prod`
34×	`add-sqr-sqrt` `*-un-lft-identity`
33×	`unpow-prod-up`
32×	`add-cube-cbrt`
27×	`prod-diff`
22×	`log-pow`
9×	`unpow-prod-down`
6×	`pow1` `log-prod`
5×	`pow-unpow` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `sin-sum` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `rem-log-exp` `pow-exp` `distribute-lft-out--` `pow-sub` `difference-of-squares` `rem-exp-log`

Counts

4 → 111

Calls

4 calls:

6.0ms	(pow (atan2 b b) (- b a))
33.0ms	(sin (log (exp (sqrt (pow (atan2 b b) (- b a))))))
19.0ms	(exp (sqrt (pow (atan2 b b) (- b a))))
25.0ms	(log (exp (sqrt (pow (atan2 b b) (- b a)))))

series204.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (atan2 b b) (- b a))
84.0ms	(sin (log (exp (sqrt (pow (atan2 b b) (- b a))))))
60.0ms	(exp (sqrt (pow (atan2 b b) (- b a))))
37.0ms	(log (exp (sqrt (pow (atan2 b b) (- b a)))))

simplify711.0ms

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	1280
1	435
0	211

prune650.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (pow (exp (sqrt (pow (atan2 b b) (- b a)))) (sqrt (pow (atan2 b b) (fma (- (sqrt a)) (sqrt a) (* (sqrt a) (sqrt a)))))))
0.0b	(exp (sqrt (pow (atan2 b b) (- b a))))
0.2b	(* (sqrt a) (sqrt a))
23.3b	(fma (- (sqrt a)) (sqrt a) (* (sqrt a) (sqrt a)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

36×	`sqrt-prod`
35×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `add-cube-cbrt`
21×	`exp-prod`
19×	`pow1`
11×	`unpow-prod-up`
9×	`prod-diff`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
7×	`log-prod` `add-exp-log`
6×	`unpow-prod-down` `add-cbrt-cube` `associate-r` `associate-l`
5×	`pow-prod-up` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`rem-log-exp` `pow-prod-down` `pow-sqr`
2×	`sqr-pow`
1×	`pow2` `pow-to-exp` `sub-neg` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `pow-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

11.0ms	(log (pow (exp (sqrt (pow (atan2 b b) (- b a)))) (sqrt (pow (atan2 b b) (fma (- (sqrt a)) (sqrt a) (* (sqrt a) (sqrt a)))))))
29.0ms	(exp (sqrt (pow (atan2 b b) (- b a))))
18.0ms	(* (sqrt a) (sqrt a))
1.0ms	(fma (- (sqrt a)) (sqrt a) (* (sqrt a) (sqrt a)))

series26.4s

Counts

4 → 12

Calls

4 calls:

26.2s	(log (pow (exp (sqrt (pow (atan2 b b) (- b a)))) (sqrt (pow (atan2 b b) (fma (- (sqrt a)) (sqrt a) (* (sqrt a) (sqrt a)))))))
65.0ms	(exp (sqrt (pow (atan2 b b) (- b a))))
25.0ms	(* (sqrt a) (sqrt a))
118.0ms	(fma (- (sqrt a)) (sqrt a) (* (sqrt a) (sqrt a)))

simplify731.0ms

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	1745
1	471
0	218

prune556.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes67.0ms

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	9
1	9
0	8

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	1833×	body	10240	exit
994.0ms	7989×	body	80	valid
799.0ms	9748×	body	80	nan
4.0ms	3×	body	2560	valid
1.0ms	3×	body	320	valid
1.0ms	1×	body	1280	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	640	valid