Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	183×	body	80	valid
5.0ms	9×	body	5120	valid
4.0ms	21×	body	2560	valid
3.0ms	18×	body	1280	valid
2.0ms	15×	body	640	valid
0.0ms	6×	body	160	valid
0.0ms	4×	body	320	valid

simplify21.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	12	15
1	19	10
2	28	10
3	36	10
4	42	10
5	44	10
done	44	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (- (hypot re im) re) 2.0))
1.5b	(- (hypot re im) re)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
5×	`pow1`
4×	`add-log-exp`
3×	`fma-neg`
2×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-pow1` `sqrt-div` `associate-*l/` `add-cbrt-cube` `flip--` `log1p-expm1-u`
1×	`sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

4.0ms	(sqrt (* (- (hypot re im) re) 2.0))
3.0ms	(- (hypot re im) re)

series242.0ms

Counts

2 → 6

Calls

2 calls:

181.0ms	(sqrt (* (- (hypot re im) re) 2.0))
61.0ms	(- (hypot re im) re)

simplify2.6s

Counts

49 → 49

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	107	626
1	229	520
2	744	437
3	4051	382
done	5000	381

prune118.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 15.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- (hypot re im) re))
0.3b	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
1.5b	(- (hypot re im) re)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`sqrt-prod`
15×	`add-cube-cbrt`
9×	`prod-diff`
8×	`pow1` `associate-l`
6×	`associate-r`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`expm1-log1p-u` `flip3--` `sqrt-pow1` `pow1/2` `fma-neg` `pow-prod-down` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 83

Calls

3 calls:

5.0ms	(sqrt (- (hypot re im) re))
13.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
3.0ms	(- (hypot re im) re)

series370.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(sqrt (- (hypot re im) re))
183.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
58.0ms	(- (hypot re im) re)

simplify471.0ms

Counts

92 → 92

Iterations

Useful iterations: done (469.0ms)

Iter	Nodes	Cost
0	160	1139
1	351	993
2	1150	892
done	5001	876

prune222.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (sqrt (- (hypot re im) re))) (* (sqrt (sqrt (- (hypot re im) re))) (sqrt 2.0)))
0.3b	(* (sqrt (sqrt (- (hypot re im) re))) (sqrt 2.0))
1.5b	(- (hypot re im) re)
1.5b	(- (hypot re im) re)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`sqrt-prod`
34×	`*-un-lft-identity`
28×	`sqrt-div`
26×	`add-cube-cbrt`
22×	`associate-l`
18×	`prod-diff`
16×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow-prod-down` `associate-*l/`
9×	`flip3--` `flip--`
8×	`add-log-exp`
7×	`associate-r`
6×	`fma-neg` `unswap-sqr`
5×	`sqrt-pow1` `pow1/2`
4×	`expm1-log1p-u` `frac-times` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sqrt-unprod`
2×	`sub-neg` `diff-log` `associate-r/` `-commutative`

Counts

4 → 136

Calls

4 calls:

35.0ms	(* (sqrt (sqrt (- (hypot re im) re))) (* (sqrt (sqrt (- (hypot re im) re))) (sqrt 2.0)))
19.0ms	(* (sqrt (sqrt (- (hypot re im) re))) (sqrt 2.0))
3.0ms	(- (hypot re im) re)
3.0ms	(- (hypot re im) re)

series503.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (sqrt (sqrt (- (hypot re im) re))) (* (sqrt (sqrt (- (hypot re im) re))) (sqrt 2.0)))
198.0ms	(* (sqrt (sqrt (- (hypot re im) re))) (sqrt 2.0))
59.0ms	(- (hypot re im) re)
58.0ms	(- (hypot re im) re)

simplify588.0ms

Counts

148 → 148

Iterations

Useful iterations: done (583.0ms)

Iter	Nodes	Cost
0	216	2495
1	498	2006
2	1579	1729
done	5000	1727

prune425.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (hypot re im) re))
0.2b	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.3b	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
1.5b	(- (hypot re im) re)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
37×	`sqrt-prod`
26×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`associate-r`
17×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow-prod-down`
9×	`associate-l` `prod-diff`
6×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-*l/` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `flip3--` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg` `sqrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`*-commutative`
1×	`sub-neg` `rem-sqrt-square` `diff-log`

Counts

4 → 119

Calls

4 calls:

5.0ms	(sqrt (- (hypot re im) re))
30.0ms	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
15.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
7.0ms	(- (hypot re im) re)

series617.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(sqrt (- (hypot re im) re))
186.0ms	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
246.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
59.0ms	(- (hypot re im) re)

simplify746.0ms

Counts

131 → 131

Iterations

Useful iterations: done (742.0ms)

Iter	Nodes	Cost
0	212	1873
1	512	1559
2	1935	1386
done	5001	1381

prune302.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.3b

regimes84.0ms

Accuracy

0% (0.2b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	11	10
done	11	10

end0.0ms

sample657.0ms

Algorithm

intervals

Results

191.0ms	6029×	body	80	valid
137.0ms	701×	body	2560	valid
75.0ms	471×	body	1280	valid
68.0ms	290×	body	5120	valid
32.0ms	268×	body	640	valid
16.0ms	158×	body	320	valid
5.0ms	83×	body	160	valid