Details

sample183.0ms

Algorithm

intervals

Results

87.0ms	63×	body	10240	exit
42.0ms	324×	body	80	nan
33.0ms	256×	body	80	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
7	2494
6	745
5	254
4	110
3	45
2	22
1	13
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite16.0ms

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` `insert-posit16` `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 → 66

Calls

3 calls:

9.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
5.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series147.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
35.0ms	(pow (sqrt (atan2 b b)) (- b a))
14.0ms	(sqrt (atan2 b b))

simplify1.8s

Counts

75 → 75

Iterations

Iter	Nodes
4	3500
3	1486
2	616
1	299
0	120

prune863.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
24×	`sqrt-prod`
22×	`unpow-prod-up`
18×	`unpow-prod-down` `prod-diff`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`pow1/2` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 122

Calls

4 calls:

12.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
12.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series128.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
49.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
22.0ms	(sqrt (atan2 b b))
20.0ms	(sqrt (atan2 b b))

simplify2.6s

Counts

134 → 134

Iterations

Iter	Nodes
4	4382
3	1816
2	698
1	326
0	124

prune1.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
4.3b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
24×	`log-prod` `sqrt-prod`
22×	`unpow-prod-up`
18×	`unpow-prod-down` `prod-diff`
9×	`pow1`
7×	`add-exp-log`
6×	`sqrt-pow1`
5×	`pow-unpow` `pow-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow1/2` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `pow-sub` `sqr-pow`
1×	`log-div` `log-pow` `sqrt-pow2` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 116

Calls

4 calls:

6.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
5.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
16.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))
93.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify972.0ms

Counts

128 → 128

Iterations

Iter	Nodes
3	2288
2	863
1	413
0	166

prune2.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
4.3b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))
4.3b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

48×	`log-prod`
28×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `add-cube-cbrt`
24×	`sqrt-prod`
22×	`unpow-prod-up`
18×	`unpow-prod-down` `prod-diff`
8×	`add-exp-log`
6×	`pow1` `rem-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `log-div` `sub-neg` `sqrt-pow1` `pow1/2` `pow-exp` `log-pow` `pow-sub` `sqr-pow`

Counts

4 → 110

Calls

4 calls:

2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
11.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))
16.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt (atan2 b b))
24.0ms	(sqrt (atan2 b b))
92.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))
109.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify1.6s

Counts

122 → 122

Iterations

Iter	Nodes
4	4090
3	1509
2	588
1	295
0	139

prune2.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes151.0ms

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
1	11
0	11

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.4s	1783×	body	10240	exit
2.1s	7990×	body	80	valid
1.7s	9901×	body	80	nan
14.0ms	3×	body	5120	valid
3.0ms	2×	body	1280	valid
2.0ms	1×	body	2560	valid
1.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid