Details

sample86.0ms

Algorithm

intervals

Results

12.0ms	214×	body	80	valid
3.0ms	13×	body	2560	valid
3.0ms	13×	body	1280	valid
2.0ms	10×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	2×	body	320	valid

simplify257.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
5	44
4	42
3	35
2	27
1	19
0	12

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.3b

localize27.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (hypot re im) re)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

14.0ms

(- (hypot re im) re)

series134.0ms

Counts

1 → 3

Calls

1 calls:

134.0ms

(- (hypot re im) re)

simplify3.6s

Counts

31 → 31

Iterations

Iter	Nodes
done	5115
5	3569
4	1349
3	619
2	237
1	130
0	61

prune204.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 9.2b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (hypot re im) re)
0.0b	(- (hypot re im) re)
0.4b	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
30×	`sqrt-prod`
25×	`add-cube-cbrt`
18×	`pow1` `prod-diff`
12×	`sqrt-div` `swap-sqr`
8×	`sqrt-pow1` `flip3--` `pow1/2` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
7×	`add-log-exp`
6×	`fma-neg` `difference-of-squares`
5×	`add-cbrt-cube` `add-exp-log` `pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`expm1-log1p-u` `pow-prod-down` `pow-sqr` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-l/` `associate-r/`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 123

Calls

3 calls:

11.0ms	(- (hypot re im) re)
10.0ms	(- (hypot re im) re)
69.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))

series288.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(- (hypot re im) re)
92.0ms	(- (hypot re im) re)
90.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))

simplify3.5s

Counts

132 → 132

Iterations

Iter	Nodes
done	5000
4	4077
3	1125
2	464
1	251
0	128

prune655.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 9.2b

localize29.0ms

Local error

Found 1 expressions with local error:

10.4b

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

4.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series165.0ms

Counts

1 → 3

Calls

1 calls:

165.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify3.2s

Counts

13 → 13

Iterations

Iter	Nodes
done	5000
5	4960
4	1418
3	455
2	135
1	52
0	28

prune138.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 9.2b

localize46.0ms

Local error

Found 3 expressions with local error:

0.4b

(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))

10.4b

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

10.4b

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 71

Calls

3 calls:

20.0ms

(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))

0.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

1.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series665.0ms

Counts

3 → 9

Calls

3 calls:

199.0ms

(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))

219.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

246.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify1.9s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
3	1071
2	313
1	154
0	73

prune415.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 9.2b

regimes192.0ms

Accuracy

0% (0.2b remaining)

Error of 13.2b against oracle of 13.0b and baseline of 13.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

587.0ms	279×	body	640	valid
524.0ms	6087×	body	80	valid
469.0ms	646×	body	2560	valid
213.0ms	512×	body	1280	valid
134.0ms	259×	body	5120	valid
31.0ms	151×	body	320	valid
9.0ms	66×	body	160	valid