Details

sample134.0ms

Algorithm

intervals

Results

45.0ms	52×	body	10240	exit
31.0ms	316×	body	80	nan
28.0ms	255×	body	80	valid
3.0ms	1×	body	5120	valid

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	115	9
5	274	9
6	837	9
7	3217	9
done	5001	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.2b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite24.0ms

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

Counts

3 → 63

Calls

3 calls:

8.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))

series127.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(pow (sqrt (atan2 b b)) (- b a))
77.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
19.0ms	(sqrt (atan2 b b))

simplify4.3s

Counts

72 → 72

Iterations

Useful iterations: 4 (3.0s)

Iter	Nodes	Cost
0	117	962
1	246	836
2	485	757
3	1274	728
4	4144	699
done	5000	699

prune240.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (atan2 b b) (* 1/2 (- b a)))
0.2b	(sin (pow (atan2 b b) (* 1/2 (- b a))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

22×	`unpow-prod-up`
18×	`prod-diff`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`distribute-rgt-in` `distribute-lft-in`
3×	`pow1` `add-exp-log` `unpow-prod-down`
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:

8.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
19.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

series163.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
124.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify2.5s

Counts

54 → 54

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	143	1154
1	307	973
2	578	837
3	1489	703
done	5000	637

prune132.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- b a) (log (sqrt (atan2 b b))))
0.4b	(fma (cos 1) (* (- b a) (log (sqrt (atan2 b b)))) (sin 1))
1.0b	(sqrt (atan2 b b))
2.0b	(log (sqrt (atan2 b b)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `log-prod`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`sqrt-prod`
11×	`pow1`
7×	`add-exp-log`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `log-pow` `add-cbrt-cube`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`associate-*l/`
1×	`rem-sqrt-square` `flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

34.0ms	(* (- b a) (log (sqrt (atan2 b b))))
0.0ms	(fma (cos 1) (* (- b a) (log (sqrt (atan2 b b)))) (sin 1))
1.0ms	(sqrt (atan2 b b))
2.0ms	(log (sqrt (atan2 b b)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (- b a) (log (sqrt (atan2 b b))))
134.0ms	(fma (cos 1) (* (- b a) (log (sqrt (atan2 b b)))) (sin 1))
20.0ms	(sqrt (atan2 b b))
97.0ms	(log (sqrt (atan2 b b)))

simplify1.9s

Counts

95 → 95

Iterations

Useful iterations: 3 (862.0ms)

Iter	Nodes	Cost
0	114	1148
1	195	1080
2	595	974
3	1923	947
done	5000	947

prune378.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(fma (cos 1) (* (- b a) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))) (sin 1))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
2.0b	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-pow1`
30×	`pow1`
22×	`log-pow`
18×	`pow1/2`
9×	`pow-prod-up`
8×	`add-sqr-sqrt`
7×	`add-exp-log`
6×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp`
1×	`pow2` `log-prod` `pow-plus` `prod-exp` `fma-udef`

Counts

4 → 74

Calls

4 calls:

0.0ms	(fma (cos 1) (* (- b a) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))) (sin 1))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
21.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(fma (cos 1) (* (- b a) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))) (sin 1))
21.0ms	(sqrt (atan2 b b))
15.0ms	(sqrt (atan2 b b))
98.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

simplify2.9s

Counts

86 → 86

Iterations

Useful iterations: 3 (191.0ms)

Iter	Nodes	Cost
0	58	888
1	89	654
2	219	608
3	763	581
4	3027	581
done	5000	581

prune453.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes40.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	9	10
done	9	10

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.0s	1799×	body	10240	exit
1.2s	7992×	body	80	valid
1.1s	9789×	body	80	nan
5.0ms	2×	body	5120	valid
4.0ms	2×	body	2560	valid
1.0ms	4×	body	160	valid