Details

sample73.0ms

Algorithm

intervals

Results

24.0ms	61×	body	10240	exit
15.0ms	348×	body	80	nan
14.0ms	256×	body	80	valid

simplify49.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	22	5
2	44	5
3	114	5
4	315	5
5	1609	5
6	5001	5
done	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

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))

rewrite21.0ms

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:

10.0ms	(pow (sqrt (atan2 b b)) (- b a))
9.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))

series94.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(pow (sqrt (atan2 b b)) (- b a))
60.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
11.0ms	(sqrt (atan2 b b))

simplify44.0ms

Counts

57 → 57

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	148	324
1	412	298
2	1346	292
3	5001	290
done	5001	290

prune119.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))
0.0b	(sin (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
16×	`pow-exp`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `prod-exp`
7×	`pow1` `pow-to-exp` `add-cube-cbrt`
6×	`sqrt-prod`
5×	`pow-unpow` `pow-pow`
4×	`add-cbrt-cube` `add-log-exp`
2×	`unpow-prod-up` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow1/2`
1×	`pow2` `sub-neg` `unpow-prod-down` `sqrt-unprod` `pow-prod-down` `pow-sqr` `pow-prod-up` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

14.0ms	(pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))
20.0ms	(sin (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series107.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))
64.0ms	(sin (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))
10.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify64.0ms

Counts

79 → 79

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	167	542
1	445	445
2	2031	428
3	5002	413
done	5002	413

prune175.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))
1.0b	(sqrt (atan2 b b))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

19.0ms	(sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))
1.0ms	(sqrt (atan2 b b))

series97.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))
11.0ms	(sqrt (atan2 b b))

simplify35.0ms

Counts

26 → 26

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	90	164
1	223	142
2	794	138
3	5001	138
done	5001	138

prune76.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

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))

rewrite5.0ms

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:

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify95.0ms

Counts

64 → 64

Iterations

Useful iterations: 7 (27.0ms)

Iter	Nodes	Cost
0	22	188
1	25	184
2	28	184
3	33	184
4	52	184
5	106	184
6	533	184
7	1765	180
8	5001	180
done	5001	180

prune213.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	7
1	12	7
done	12	7

end0.0ms

sample2.2s

Algorithm

intervals

Results

804.0ms	1848×	body	10240	exit
458.0ms	9800×	body	80	nan
440.0ms	7991×	body	80	valid
3.0ms	1×	body	5120	valid
2.0ms	2×	body	2560	valid
2.0ms	3×	body	1280	valid
1.0ms	2×	body	640	valid
0.0ms	1×	body	320	valid