Details

sample50.0ms

Algorithm

intervals

Results

15.0ms	197×	body	80	valid
10.0ms	23×	body	2560	valid
7.0ms	16×	body	1280	valid
6.0ms	10×	body	5120	valid
2.0ms	6×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	31
3	31
2	29
1	24
0	12

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.5b	(+ (hypot re im) re)

rewrite15.0ms

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-+` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

2 → 34

Calls

2 calls:

6.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
9.0ms	(+ (hypot re im) re)

series389.0ms

Counts

2 → 6

Calls

2 calls:

295.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
94.0ms	(+ (hypot re im) re)

simplify954.0ms

Counts

40 → 40

Iterations

Iter	Nodes
done	2010
4	2010
3	1359
2	470
1	176
0	77

prune365.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.7b

localize19.0ms

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))
14.6b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite7.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 57

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
4.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series828.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(sqrt (hypot re im))
136.0ms	(sqrt (hypot re im))
349.0ms	(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)

simplify1.7s

Counts

69 → 69

Iterations

Iter	Nodes
done	2004
4	2004
3	1844
2	531
1	198
0	93

prune777.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) 2.0))
0.4b	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
14.6b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
14.6b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
24×	`add-sqr-sqrt`
19×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`sqrt-pow1`
9×	`pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `pow-prod-down` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-sqr`
2×	`fma-udef`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 89

Calls

4 calls:

38.0ms	(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) 2.0))
23.0ms	(* (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)

series1.0s

Counts

4 → 12

Calls

4 calls:

368.0ms	(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) 2.0))
225.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
189.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
221.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.1s

Counts

101 → 101

Iterations

Iter	Nodes
done	2006
4	2006
3	1389
2	473
1	232
0	107

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.6b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) 2.0))
0.4b	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
14.6b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
14.6b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
24×	`add-sqr-sqrt`
19×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`sqrt-pow1`
9×	`pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `pow-prod-down` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-sqr`
2×	`fma-udef`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 89

Calls

4 calls:

37.0ms	(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) 2.0))
17.0ms	(* (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)

series954.0ms

Counts

4 → 12

Calls

4 calls:

361.0ms	(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) 2.0))
205.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
171.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
217.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.0s

Counts

101 → 101

Iterations

Iter	Nodes
done	2006
4	2006
3	1389
2	473
1	232
0	107

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.6b

regimes201.0ms

Accuracy

0% (0.3b remaining)

Error of 14.2b against oracle of 13.9b and baseline of 14.2b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

802.0ms	542×	body	1280	valid
736.0ms	5898×	body	80	valid
606.0ms	736×	body	2560	valid
268.0ms	308×	body	5120	valid
113.0ms	261×	body	640	valid
54.0ms	168×	body	320	valid
17.0ms	87×	body	160	valid