Details

sample299.0ms

Algorithm

intervals

Results

96.0ms	256×	body	80	valid
56.0ms	63×	body	10240	exit
41.0ms	371×	body	80	nan

simplify651.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

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))

rewrite35.0ms

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:

19.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
7.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sqrt (atan2 b b))

series169.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
32.0ms	(pow (sqrt (atan2 b b)) (- b a))
37.0ms	(sqrt (atan2 b b))

simplify693.0ms

Counts: 57 → 57

prune224.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-prod`
78×	`unpow-prod-down`
76×	`add-sqr-sqrt`
25×	`unswap-sqr`
23×	`swap-sqr`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
15×	`associate-r` `associate-l`
14×	`sqr-pow`
12×	`unpow-prod-up`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`pow-sub` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 136

Calls

4 calls:

61.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
89.0ms	(* (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))

series219.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
57.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
20.0ms	(sqrt (atan2 b b))
21.0ms	(sqrt (atan2 b b))

simplify744.0ms

Counts: 148 → 148

prune522.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
0.0b	(pow (sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))) 3)
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-prod`
81×	`unpow-prod-down`
79×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity` `unswap-sqr`
23×	`swap-sqr`
17×	`add-exp-log`
15×	`associate-r` `associate-l` `sqr-pow`
12×	`unpow-prod-up`
9×	`prod-exp`
7×	`pow1` `pow-to-exp` `pow-exp` `add-cbrt-cube`
6×	`sub-neg`
4×	`pow-sub` `add-log-exp`
3×	`pow-unpow` `cube-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `cube-mult` `frac-times` `pow-pow` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 152

Calls

4 calls:

95.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
29.0ms	(pow (sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))) 3)
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series294.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
200.0ms	(pow (sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))) 3)
17.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify1.1s

Counts: 164 → 164

prune609.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series70.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))
30.0ms	(sqrt (atan2 b b))

simplify2.3s

Counts: 64 → 64

prune391.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes53.0ms

Accuracy

655.6% (-0.0b remaining)

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

bsearch0.0ms

simplify1.4s

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.8s	7992×	body	80	valid
1.7s	1903×	body	10240	exit
1.3s	9890×	body	80	nan
4.0ms	2×	body	2560	valid
2.0ms	4×	body	320	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid