Details

sample56.0ms

Algorithm

intervals

Results

13.0ms	182×	body	80	valid
12.0ms	27×	body	2560	valid
7.0ms	20×	body	1280	valid
6.0ms	11×	body	5120	valid
3.0ms	11×	body	640	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	320	valid

simplify12.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize40.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ (hypot re im) re) 2.0)
0.8b	(+ (hypot re im) re)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-log-exp`
3×	`fma-def` `associate-r`
2×	`expm1-log1p-u` `flip3-+` `associate-*l/` `flip-+` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `sum-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 40

Calls

2 calls:

25.0ms	(* (+ (hypot re im) re) 2.0)
9.0ms	(+ (hypot re im) re)

series167.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(* (+ (hypot re im) re) 2.0)
87.0ms	(+ (hypot re im) re)

simplify827.0ms

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	558
1	146
0	64

prune355.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 15.5b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
18.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

6.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series432.0ms

Counts

2 → 6

Calls

2 calls:

205.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
227.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify2.5s

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
3	2623
2	378
1	111
0	55

prune282.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 15.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
17.8b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

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

series784.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (hypot re im))
188.0ms	(cbrt (hypot re im))
190.0ms	(cbrt (hypot re im))
245.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

simplify2.7s

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
4	3776
3	675
2	188
1	82
0	49

prune499.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 15.5b

localize60.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt (hypot re im)))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
17.8b	(fma (* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`fma-udef`

Counts

4 → 52

Calls

4 calls:

9.0ms	(cbrt (sqrt (hypot re im)))
1.0ms	(cbrt (hypot re im))
2.0ms	(cbrt (hypot re im))
1.0ms	(fma (* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

series711.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(cbrt (sqrt (hypot re im)))
162.0ms	(cbrt (hypot re im))
150.0ms	(cbrt (hypot re im))
206.0ms	(fma (* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

simplify1.6s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	1293
2	358
1	140
0	80

prune562.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 15.5b

regimes402.0ms

Accuracy

0% (0.2b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.0s

Algorithm

intervals

Results

756.0ms	6016×	body	80	valid
332.0ms	669×	body	2560	valid
228.0ms	342×	body	5120	valid
208.0ms	492×	body	1280	valid
136.0ms	274×	body	640	valid
66.0ms	127×	body	320	valid
10.0ms	80×	body	160	valid