Details

sample68.0ms

Algorithm

intervals

Results

19.0ms	190×	body	80	valid
16.0ms	25×	body	2560	valid
10.0ms	12×	body	5120	valid
8.0ms	15×	body	1280	valid
4.0ms	8×	body	640	valid
1.0ms	5×	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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize48.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.3b	(+ (hypot re im) re)

rewrite22.0ms

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:

12.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
9.0ms	(+ (hypot re im) re)

series346.0ms

Counts

2 → 6

Calls

2 calls:

261.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
84.0ms	(+ (hypot re im) re)

simplify976.0ms

Counts

40 → 40

Iterations

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

prune393.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 12.6b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
16.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
2×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

2 → 25

Calls

2 calls:

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)

series551.0ms

Counts

2 → 6

Calls

2 calls:

328.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
222.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.5s

Counts

31 → 31

Iterations

Iter	Nodes
done	2001
4	2001
3	1086
2	335
1	132
0	63

prune293.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.6b

localize22.0ms

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)))
16.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
16.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite47.0ms

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:

36.0ms	(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))
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)

series825.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(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))
189.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
196.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
155.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.2s

Counts

101 → 101

Iterations

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

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
16.1b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

2.0ms	(cbrt (hypot re im))
2.0ms	(cbrt (hypot re im))
13.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
0.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

series665.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt (hypot re im))
178.0ms	(cbrt (hypot re im))
153.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
180.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

simplify1.2s

Counts

94 → 94

Iterations

Iter	Nodes
done	2037
4	2037
3	1157
2	436
1	185
0	94

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.6b

regimes218.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.3s	5970×	body	80	valid
653.0ms	703×	body	2560	valid
375.0ms	307×	body	5120	valid
279.0ms	481×	body	1280	valid
167.0ms	289×	body	640	valid
58.0ms	167×	body	320	valid
18.0ms	83×	body	160	valid