Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	190×	body	80	valid
5.0ms	22×	body	1280	valid
5.0ms	16×	body	2560	valid
3.0ms	9×	body	5120	valid
3.0ms	11×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify43.0ms

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* (+ (hypot re im) re) 2.0))
0.6b	(+ (hypot re im) re)

rewrite12.0ms

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` `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 → 42

Calls

3 calls:

0.0ms	(hypot re im)
6.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
5.0ms	(+ (hypot re im) re)

series417.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(hypot re im)
248.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
108.0ms	(+ (hypot re im) re)

simplify1.8s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
3	3673
2	612
1	187
0	86

prune354.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ re (hypot re im)))
0.0b	(hypot re im)
0.4b	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
0.6b	(+ re (hypot re im))

rewrite49.0ms

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` `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 → 81

Calls

4 calls:

18.0ms	(sqrt (+ re (hypot re im)))
1.0ms	(hypot re im)
23.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
5.0ms	(+ re (hypot re im))

series580.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(sqrt (+ re (hypot re im)))
54.0ms	(hypot re im)
290.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
80.0ms	(+ re (hypot re im))

simplify707.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	1278
1	307
0	135

prune526.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.7b

localize29.0ms

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))
15.7b	(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` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef` `sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

4 → 43

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
7.0ms	(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)

series662.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(hypot re im)
72.0ms	(hypot re im)
333.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
190.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.5s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
3	2477
2	481
1	149
0	74

prune422.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 13.7b

localize35.0ms

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)))
15.7b	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (sqrt (hypot re im)) re)

rewrite24.0ms

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` `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 → 78

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
18.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
1.0ms	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (sqrt (hypot re im)) re)

series728.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(cbrt (hypot re im))
181.0ms	(cbrt (hypot re im))
218.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
169.0ms	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (sqrt (hypot re im)) re)

simplify1.0s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	820
1	208
0	98

prune572.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 13.7b

regimes288.0ms

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

sample2.0s

Algorithm

intervals

Results

1.0s	5974×	body	80	valid
246.0ms	696×	body	2560	valid
191.0ms	501×	body	1280	valid
131.0ms	301×	body	5120	valid
92.0ms	275×	body	640	valid
27.0ms	169×	body	320	valid
10.0ms	84×	body	160	valid