Details

sample69.0ms

Algorithm

intervals

Results

19.0ms	188×	body	80	valid
16.0ms	26×	body	2560	valid
9.0ms	16×	body	1280	valid
6.0ms	14×	body	640	valid
4.0ms	5×	body	5120	valid
2.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

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

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.2b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.2b	(+ (hypot re im) re)

rewrite11.0ms

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))
5.0ms	(+ (hypot re im) re)

series367.0ms

Counts

2 → 6

Calls

2 calls:

283.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
83.0ms	(+ (hypot re im) re)

simplify2.6s

Counts

40 → 40

Iterations

Iter	Nodes
done	5000
3	1650
2	478
1	176
0	77

prune215.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 15.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.3b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
16.6b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite11.0ms

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))
8.0ms	(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)

series737.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(sqrt (hypot re im))
117.0ms	(sqrt (hypot re im))
307.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
174.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify3.9s

Counts

69 → 69

Iterations

Iter	Nodes
done	5001
3	2108
2	542
1	198
0	93

prune407.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.1b	(sqrt (sqrt (hypot re im)))
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
16.6b	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

86×	`sqrt-prod`
54×	`add-sqr-sqrt`
40×	`sqrt-pow1`
31×	`pow1`
20×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 133

Calls

4 calls:

2.0ms	(sqrt (sqrt (hypot re im)))
2.0ms	(sqrt (sqrt (hypot re im)))
12.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)

series636.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(sqrt (sqrt (hypot re im)))
148.0ms	(sqrt (sqrt (hypot re im)))
118.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
186.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)

simplify1.7s

Counts

145 → 145

Iterations

Iter	Nodes
done	5000
3	1622
2	600
1	276
0	133

prune681.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.9b

localize67.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
16.6b	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)
16.6b	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

132×	`sqrt-prod`
88×	`add-sqr-sqrt`
64×	`sqrt-pow1`
50×	`pow1`
32×	`pow1/2`
30×	`swap-sqr`
28×	`*-un-lft-identity` `add-cube-cbrt`
18×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
10×	`pow-prod-down` `pow-sqr`
8×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 178

Calls

4 calls:

25.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
25.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)
1.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)

series669.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
129.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
198.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)
204.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)

simplify2.5s

Counts

190 → 190

Iterations

Iter	Nodes
done	5000
4	3939
3	1242
2	514
1	238
0	114

prune789.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 14.9b

regimes217.0ms

Accuracy

0% (0.3b remaining)

Error of 12.8b against oracle of 12.6b and baseline of 12.8b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	6092×	body	80	valid
482.0ms	657×	body	2560	valid
268.0ms	456×	body	1280	valid
253.0ms	278×	body	5120	valid
164.0ms	282×	body	640	valid
49.0ms	160×	body	320	valid
16.0ms	75×	body	160	valid