Details

sample140.0ms

Algorithm

intervals

Results

46.0ms	47×	body	10240	exit
32.0ms	255×	body	80	valid
32.0ms	293×	body	80	nan
5.0ms	1×	body	5120	valid

simplify606.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	444
4	117
3	45
2	22
1	13
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
0.3b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite30.0ms

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

Counts

3 → 63

Calls

3 calls:

7.0ms	(pow (sqrt (atan2 b b)) (- b a))
17.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(sqrt (atan2 b b))

series146.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(pow (sqrt (atan2 b b)) (- b a))
96.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
19.0ms	(sqrt (atan2 b b))

simplify793.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1102
1	315
0	117

prune372.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`sqrt-prod`
11×	`unpow-prod-up`
9×	`pow1` `unpow-prod-down` `prod-diff`
6×	`sqrt-pow1`
5×	`pow-unpow` `pow-pow` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow1/2` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow-to-exp` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

15.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
47.0ms	(sin (* (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))

series206.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
123.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
13.0ms	(sqrt (atan2 b b))
24.0ms	(sqrt (atan2 b b))

simplify1.1s

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	1427
1	391
0	146

prune539.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize87.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
3.6b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod`
18×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
15×	`sqrt-prod`
11×	`unpow-prod-up`
9×	`unpow-prod-down` `prod-diff`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `log-div` `sub-neg` `pow-exp` `log-pow` `pow-sub` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

71.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
14.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
12.0ms	(sqrt (atan2 b b))
17.0ms	(sqrt (atan2 b b))
152.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify622.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	1032
1	363
0	164

prune620.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
0.3b	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
0.3b	(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0b	(sqrt (atan2 b b))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

14.0ms	(exp (log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
18.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
12.0ms	(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0ms	(sqrt (atan2 b b))

series457.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(exp (log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))))
125.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
188.0ms	(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
16.0ms	(sqrt (atan2 b b))

simplify863.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
3	1425
2	384
1	158
0	88

prune470.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes131.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.5s	1888×	body	10240	exit
1.2s	9645×	body	80	nan
881.0ms	7988×	body	80	valid
29.0ms	5×	body	5120	valid
2.0ms	6×	body	160	valid
0.0ms	1×	body	320	valid