Details

sample253.0ms

Algorithm

intervals

Results

71.0ms	256×	body	80	valid
49.0ms	56×	body	10240	exit
35.0ms	323×	body	80	nan

simplify9.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	117	9
5	444	9
6	4596	9
done	5001	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

2 → 24

Calls

2 calls:

19.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(sqrt (atan2 b b))

series132.0ms

Counts

2 → 6

Calls

2 calls:

111.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
21.0ms	(sqrt (atan2 b b))

simplify1.0s

Counts

30 → 30

Iterations

Useful iterations: 4 (124.0ms)

Iter	Nodes	Cost
0	41	268
1	66	253
2	112	233
3	203	225
4	396	224
5	889	224
done	5000	224

prune122.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (sin (pow (sqrt (atan2 b b)) (- b a))))
0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.0b	(expm1 (log1p (sin (pow (sqrt (atan2 b b)) (- b a)))))
1.0b	(sqrt (atan2 b b))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `log1p-udef` `expm1-log1p` `sqrt-pow1` `pow1/2` `log1p-expm1` `expm1-udef`

Counts

4 → 46

Calls

4 calls:

1.0ms	(log1p (sin (pow (sqrt (atan2 b b)) (- b a))))
25.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(expm1 (log1p (sin (pow (sqrt (atan2 b b)) (- b a)))))
3.0ms	(sqrt (atan2 b b))

series422.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(log1p (sin (pow (sqrt (atan2 b b)) (- b a))))
104.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
150.0ms	(expm1 (log1p (sin (pow (sqrt (atan2 b b)) (- b a)))))
29.0ms	(sqrt (atan2 b b))

simplify1.9s

Counts

58 → 58

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	68	669
1	114	627
2	203	563
3	376	546
4	783	539
5	1695	531
done	5000	530

prune251.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `exp-prod`
5×	`add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `rem-exp-log`

Counts

4 → 54

Calls

4 calls:

27.0ms	(exp (sin (pow (sqrt (atan2 b b)) (- b a))))
14.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
26.0ms	(log (exp (sin (pow (sqrt (atan2 b b)) (- b a)))))
3.0ms	(sqrt (atan2 b b))

series305.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(exp (sin (pow (sqrt (atan2 b b)) (- b a))))
101.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
89.0ms	(log (exp (sin (pow (sqrt (atan2 b b)) (- b a)))))
17.0ms	(sqrt (atan2 b b))

simplify2.6s

Counts

66 → 66

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	77	796
1	132	741
2	263	673
3	555	645
4	1178	642
5	2320	641
done	5000	640

prune294.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.3b	(log (cbrt (pow (exp (sin (pow (sqrt (atan2 b b)) (- b a)))) 3)))
0.3b	(pow (exp (sin (pow (sqrt (atan2 b b)) (- b a)))) 3)
1.0b	(sqrt (atan2 b b))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

15×	`log-prod`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-prod`
7×	`pow1`
6×	`unpow-prod-down` `cube-prod`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `exp-prod` `sqrt-prod`
2×	`cube-mult` `unpow3` `log-pow` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `rem-log-exp` `pow-exp` `rem-cube-cbrt`

Counts

4 → 79

Calls

4 calls:

12.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
28.0ms	(log (cbrt (pow (exp (sin (pow (sqrt (atan2 b b)) (- b a)))) 3)))
40.0ms	(pow (exp (sin (pow (sqrt (atan2 b b)) (- b a)))) 3)
2.0ms	(sqrt (atan2 b b))

series422.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
91.0ms	(log (cbrt (pow (exp (sin (pow (sqrt (atan2 b b)) (- b a)))) 3)))
222.0ms	(pow (exp (sin (pow (sqrt (atan2 b b)) (- b a)))) 3)
12.0ms	(sqrt (atan2 b b))

simplify811.0ms

Counts

91 → 91

Iterations

Useful iterations: done (807.0ms)

Iter	Nodes	Cost
0	121	1537
1	260	1312
2	976	1166
done	5001	1128

prune408.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 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

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
done	7	9

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.5s	1840×	body	10240	exit
1.2s	9702×	body	80	nan
1.0s	7988×	body	80	valid
8.0ms	2×	body	5120	valid
2.0ms	7×	body	160	valid
2.0ms	2×	body	1280	valid
0.0ms	1×	body	320	valid