Details

sample66.0ms

Algorithm

intervals

Results

21.0ms	203×	body	80	valid
15.0ms	21×	body	2560	valid
10.0ms	12×	body	5120	valid
6.0ms	12×	body	1280	valid
2.0ms	5×	body	640	valid
1.0ms	2×	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: 10.6b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `*-un-lft-identity`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`+-commutative` `hypot-udef` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

3 → 45

Calls

3 calls:

0.0ms	(hypot re im)
5.0ms	(+ (hypot re im) re)
7.0ms	(sqrt (* (+ (hypot re im) re) 2.0))

series462.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(hypot re im)
76.0ms	(+ (hypot re im) re)
309.0ms	(sqrt (* (+ (hypot re im) re) 2.0))

simplify3.6s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
4	4953
3	1425
2	487
1	190
0	89

prune293.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (+ (hypot re im) re))
0.2b	(+ (hypot re im) re)
0.4b	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`sqrt-prod`
10×	`add-cube-cbrt`
9×	`pow1`
7×	`associate-l`
6×	`add-cbrt-cube` `associate-r` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out`
2×	`associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `hypot-udef` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

4 → 85

Calls

4 calls:

0.0ms	(hypot re im)
10.0ms	(sqrt (+ (hypot re im) re))
9.0ms	(+ (hypot re im) re)
30.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

series591.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(hypot re im)
171.0ms	(sqrt (+ (hypot re im) re))
81.0ms	(+ (hypot re im) re)
251.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

simplify2.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	2518
2	830
1	311
0	139

prune520.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.2b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
13.1b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(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)

series670.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(hypot re im)
61.0ms	(hypot re im)
339.0ms	(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)

simplify2.7s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
4	3588
3	1106
2	373
1	152
0	77

prune381.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* (fma (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (sqrt (hypot re im)) re) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
13.1b	(fma (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (sqrt (hypot re im)) re)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

0.0ms	(hypot re im)
4.0ms	(sqrt (* (fma (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (sqrt (hypot re im)) re) 2.0))
9.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0ms	(fma (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (sqrt (hypot re im)) re)

series700.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(hypot re im)
360.0ms	(sqrt (* (fma (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (sqrt (hypot re im)) re) 2.0))
80.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
198.0ms	(fma (sqrt (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (sqrt (hypot re im)) re)

simplify1.8s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	1351
2	496
1	247
0	121

prune490.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.2b

regimes162.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.1b and baseline of 13.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	6025×	body	80	valid
602.0ms	711×	body	2560	valid
330.0ms	488×	body	1280	valid
278.0ms	294×	body	5120	valid
119.0ms	275×	body	640	valid
50.0ms	145×	body	320	valid
13.0ms	62×	body	160	valid