Details

sample55.0ms

Algorithm

intervals

Results

15.0ms	196×	body	80	valid
10.0ms	22×	body	2560	valid
6.0ms	16×	body	1280	valid
4.0ms	7×	body	5120	valid
2.0ms	6×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.4b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.7b	(+ (hypot re im) re)

rewrite32.0ms

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:

7.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
25.0ms	(+ (hypot re im) re)

series337.0ms

Counts

2 → 6

Calls

2 calls:

271.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
66.0ms	(+ (hypot re im) re)

simplify3.4s

Counts

40 → 40

Iterations

Iter	Nodes
done	5000
4	4643
3	1359
2	470
1	176
0	77

prune228.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.2b

localize32.0ms

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))
14.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite14.0ms

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:

2.0ms	(sqrt (hypot re im))
2.0ms	(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)

series779.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt (hypot re im))
109.0ms	(sqrt (hypot re im))
333.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
231.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify2.4s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	1844
2	531
1	198
0	93

prune448.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
0.4b	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
14.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
14.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite11.0ms

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` `insert-posit16` `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 → 90

Calls

4 calls:

1.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
9.0ms	(* (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)

series847.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
219.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
202.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
206.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify3.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
4	4575
3	1097
2	405
1	204
0	92

prune511.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.2b

localize34.0ms

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))))
14.4b	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) re)

rewrite29.0ms

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:

4.0ms	(sqrt (sqrt (hypot re im)))
4.0ms	(sqrt (sqrt (hypot re im)))
18.0ms	(* (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)

series607.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(sqrt (sqrt (hypot re im)))
156.0ms	(sqrt (sqrt (hypot re im)))
121.0ms	(* (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)

simplify3.1s

Counts

145 → 145

Iterations

Iter	Nodes
done	5000
4	4837
3	1436
2	575
1	276
0	133

prune585.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 12.2b

regimes286.0ms

Accuracy

0% (0.3b remaining)

Error of 13.6b against oracle of 13.3b and baseline of 13.6b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

964.0ms	5990×	body	80	valid
392.0ms	693×	body	2560	valid
243.0ms	505×	body	1280	valid
189.0ms	290×	body	5120	valid
80.0ms	292×	body	640	valid
29.0ms	147×	body	320	valid
11.0ms	83×	body	160	valid