Details

sample124.0ms

Algorithm

intervals

Results

47.0ms	256×	body	80	valid
35.0ms	68×	body	10240	exit
21.0ms	319×	body	80	nan

simplify3.4s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.0b	(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)))
2.0ms	(sqrt (atan2 b b))

series109.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(pow (sqrt (atan2 b b)) (- b a))
73.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
12.0ms	(sqrt (atan2 b b))

simplify2.7s

Counts

72 → 72

Iterations

Useful iterations: 4 (1.8s)

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

prune151.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 9

Calls

1 calls:

22.0ms

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

series62.0ms

Counts

1 → 3

Calls

1 calls:

62.0ms

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

simplify2.0s

Counts

12 → 12

Iterations

Useful iterations: 4 (275.0ms)

Iter	Nodes	Cost
0	33	182
1	68	181
2	166	161
3	441	139
4	949	135
5	1781	135
done	5000	135

prune286.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff`
5×	`pow1` `add-exp-log` `pow-unpow` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down`
1×	`pow-to-exp` `sub-neg` `log1p-udef` `expm1-log1p` `pow-pow` `log1p-expm1` `pow-exp` `distribute-lft-out--` `expm1-udef` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

7.0ms	(pow (atan2 b b) (- b a))
0.0ms	(log1p (expm1 (sin (sqrt (pow (atan2 b b) (- b a))))))
12.0ms	(sin (sqrt (pow (atan2 b b) (- b a))))
0.0ms	(expm1 (sin (sqrt (pow (atan2 b b) (- b a)))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (atan2 b b) (- b a))
112.0ms	(log1p (expm1 (sin (sqrt (pow (atan2 b b) (- b a))))))
71.0ms	(sin (sqrt (pow (atan2 b b) (- b a))))
116.0ms	(expm1 (sin (sqrt (pow (atan2 b b) (- b a)))))

simplify1.3s

Counts

76 → 76

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	133	1134
1	287	1002
2	630	889
3	1802	849
done	5001	801

prune194.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (sqrt (pow (atan2 b b) (- b a))))
0.0b	(expm1 (sin (sqrt (pow (atan2 b b) (- b a)))))
0.0b	(expm1 (sin (sqrt (pow (atan2 b b) (- b a)))))
0.3b	(* (sqrt (expm1 (sin (sqrt (pow (atan2 b b) (- b a)))))) (sqrt (expm1 (sin (sqrt (pow (atan2 b b) (- b a)))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`expm1-log1p` `expm1-udef`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

12.0ms	(sin (sqrt (pow (atan2 b b) (- b a))))
1.0ms	(expm1 (sin (sqrt (pow (atan2 b b) (- b a)))))
0.0ms	(expm1 (sin (sqrt (pow (atan2 b b) (- b a)))))
17.0ms	(* (sqrt (expm1 (sin (sqrt (pow (atan2 b b) (- b a)))))) (sqrt (expm1 (sin (sqrt (pow (atan2 b b) (- b a)))))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sin (sqrt (pow (atan2 b b) (- b a))))
109.0ms	(expm1 (sin (sqrt (pow (atan2 b b) (- b a)))))
109.0ms	(expm1 (sin (sqrt (pow (atan2 b b) (- b a)))))
111.0ms	(* (sqrt (expm1 (sin (sqrt (pow (atan2 b b) (- b a)))))) (sqrt (expm1 (sin (sqrt (pow (atan2 b b) (- b a)))))))

simplify2.5s

Counts

94 → 94

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	94	2032
1	179	1418
2	481	1256
3	1429	1184
4	4038	1098
done	5000	1095

prune236.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

Details

sample124.0ms

simplify3.4s

prune3.0ms

localize10.0ms

rewrite24.0ms

series109.0ms

simplify2.7s

prune151.0ms

localize10.0ms

rewrite22.0ms

series62.0ms

simplify2.0s

prune286.0ms

localize12.0ms

rewrite21.0ms

series318.0ms

simplify1.3s

prune194.0ms

localize16.0ms

rewrite32.0ms

series403.0ms

simplify2.5s

prune236.0ms

regimes1.0ms