Details

sample64.0ms

Algorithm

intervals

Results

15.0ms	187×	body	80	valid
13.0ms	28×	body	2560	valid
8.0ms	21×	body	1280	valid
5.0ms	9×	body	5120	valid
2.0ms	5×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	32
3	32
2	30
1	24
0	12

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.8b	(+ (hypot re im) re)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `sqrt-div` `associate-*l/` `add-exp-log` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

2 → 32

Calls

2 calls:

7.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
19.0ms	(+ (hypot re im) re)

series378.0ms

Counts

2 → 6

Calls

2 calls:

282.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
96.0ms	(+ (hypot re im) re)

simplify2.0s

Counts

38 → 38

Iterations

Iter	Nodes
done	5000
3	3748
2	604
1	174
0	75

prune225.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
0.8b	(+ (hypot re im) re)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `sqrt-prod`
7×	`associate-l` `add-cube-cbrt`
6×	`pow1` `associate-r`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp` `unswap-sqr`
3×	`fma-def` `pow-prod-down`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `associate-*l/` `flip-+` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

2 → 52

Calls

2 calls:

21.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
5.0ms	(+ (hypot re im) re)

series319.0ms

Counts

2 → 6

Calls

2 calls:

244.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
74.0ms	(+ (hypot re im) re)

simplify1.4s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	1008
1	234
0	99

prune360.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
17.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

2.0ms	(sqrt (hypot re im))
2.0ms	(sqrt (hypot re im))
7.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series730.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (hypot re im))
132.0ms	(sqrt (hypot re im))
306.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
204.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify2.6s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
3	4353
2	709
1	195
0	90

prune441.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.4b	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
17.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
17.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
11.0ms	(* (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)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series715.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(sqrt (hypot re im))
178.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
192.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
200.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.3s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	897
1	217
0	98

prune567.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 14.1b

regimes319.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample1.9s

Algorithm

intervals

Results

573.0ms	309×	body	5120	valid
497.0ms	6046×	body	80	valid
293.0ms	678×	body	2560	valid
279.0ms	485×	body	1280	valid
67.0ms	274×	body	640	valid
24.0ms	133×	body	320	valid
9.0ms	75×	body	160	valid