Details

sample277.0ms

Algorithm

intervals

Results

52.0ms	51×	body	10240	exit
40.0ms	336×	body	80	nan
32.0ms	256×	body	80	valid

simplify672.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.1b	(pow (sqrt (atan2 b b)) (- b a))
1.0b	(sqrt (atan2 b b))

rewrite37.0ms

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:

22.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
7.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sqrt (atan2 b b))

series211.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
47.0ms	(pow (sqrt (atan2 b b)) (- b a))
32.0ms	(sqrt (atan2 b b))

simplify786.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1098
1	315
0	117

prune365.0ms

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

rewrite23.0ms

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:

14.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
6.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

series141.0ms

Counts

2 → 6

Calls

2 calls:

109.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
31.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

simplify821.0ms

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
2	1239
1	361
0	144

prune176.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (* (pow (atan2 b b) (* 1/2 (- (pow (cbrt b) 3) a))) (pow (atan2 b b) (* 1/2 (+ (- a) a)))))
0.0b	(pow (atan2 b b) (* 1/2 (- (pow (cbrt b) 3) a)))
0.6b	(cbrt b)
0.7b	(pow (cbrt b) 3)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

112×	`unpow-prod-up`
108×	`prod-diff`
77×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
56×	`distribute-rgt-in` `distribute-lft-in`
45×	`cbrt-prod` `unpow-prod-down`
42×	`cube-prod`
8×	`sqr-pow`
7×	`cube-mult` `unpow3`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow`
2×	`pow-to-exp` `sub-neg` `pow1/3` `pow-exp`
1×	`rem-cube-cbrt`

Counts

4 → 183

Calls

4 calls:

66.0ms	(sin (* (pow (atan2 b b) (* 1/2 (- (pow (cbrt b) 3) a))) (pow (atan2 b b) (* 1/2 (+ (- a) a)))))
22.0ms	(pow (atan2 b b) (* 1/2 (- (pow (cbrt b) 3) a)))
1.0ms	(cbrt b)
3.0ms	(pow (cbrt b) 3)

series815.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(sin (* (pow (atan2 b b) (* 1/2 (- (pow (cbrt b) 3) a))) (pow (atan2 b b) (* 1/2 (+ (- a) a)))))
47.0ms	(pow (atan2 b b) (* 1/2 (- (pow (cbrt b) 3) a)))
300.0ms	(cbrt b)
353.0ms	(pow (cbrt b) 3)

simplify2.1s

Counts

195 → 195

Iterations

Iter	Nodes
done	5000
2	3565
1	965
0	334

prune537.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

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))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
24×	`sqrt-prod`
22×	`unpow-prod-up`
18×	`unpow-prod-down` `prod-diff`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`pow1/2` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

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

series132.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
49.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
18.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify827.0ms

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1255
1	345
0	122

prune610.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes96.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.6s	1752×	body	10240	exit
1.6s	9700×	body	80	nan
1.5s	7988×	body	80	valid
6.0ms	1×	body	5120	valid
3.0ms	2×	body	1280	valid
2.0ms	2×	body	2560	valid
1.0ms	4×	body	160	valid
1.0ms	2×	body	640	valid
0.0ms	1×	body	320	valid