Details

sample145.0ms

Algorithm

intervals

Results

41.0ms	19×	body	1280	valid
16.0ms	199×	body	80	valid
7.0ms	14×	body	5120	valid
6.0ms	14×	body	2560	valid
2.0ms	6×	body	640	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	320	valid

simplify42.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	44
5	44
4	42
3	35
2	27
1	19
0	12

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.7b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.0b	(hypot re im)
0.9b	(- (hypot re im) re)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow1`
5×	`add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3--` `sqrt-div` `associate-*l/` `flip--`
1×	`hypot-udef` `sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 56

Calls

3 calls:

17.0ms	(sqrt (* (- (hypot re im) re) 2.0))
0.0ms	(hypot re im)
13.0ms	(- (hypot re im) re)

series490.0ms

Counts

3 → 9

Calls

3 calls:

296.0ms	(sqrt (* (- (hypot re im) re) 2.0))
67.0ms	(hypot re im)
127.0ms	(- (hypot re im) re)

simplify3.2s

Counts

65 → 65

Iterations

Iter	Nodes
4	5586
3	1672
2	519
1	232
0	118

prune638.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0b	(hypot re im)
0.0b	(hypot re im)
13.9b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite12.0ms

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:

9.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0ms	(hypot re im)
0.0ms	(hypot re im)
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series683.0ms

Counts

4 → 12

Calls

4 calls:

359.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
52.0ms	(hypot re im)
78.0ms	(hypot re im)
193.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify2.0s

Counts

59 → 59

Iterations

Iter	Nodes
4	4129
3	1236
2	399
1	159
0	81

prune596.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.6b

localize53.0ms

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))
13.9b	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (- re))

rewrite3.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (- re))

series699.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (hypot re im))
184.0ms	(cbrt (hypot re im))
171.0ms	(cbrt (hypot re im))
193.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (- re))

simplify869.0ms

Counts

65 → 65

Iterations

Iter	Nodes
4	2008
3	715
2	241
1	109
0	61

prune910.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 10.6b

localize66.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))
13.9b	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (cbrt (cbrt (hypot re im)))))) (- re))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`cbrt-prod`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 51

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
4.0ms	(cbrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (cbrt (cbrt (hypot re im)))))) (- re))

series758.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt (hypot re im))
154.0ms	(cbrt (hypot re im))
188.0ms	(cbrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))
225.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (cbrt (cbrt (hypot re im)))))) (- re))

simplify1.8s

Counts

63 → 63

Iterations

Iter	Nodes
4	2994
3	1095
2	377
1	164
0	86

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 10.5b

regimes222.0ms

Accuracy

0% (0.3b remaining)

Error of 13.8b against oracle of 13.5b and baseline of 13.8b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	11
1	11
0	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

784.0ms	521×	body	1280	valid
754.0ms	5922×	body	80	valid
559.0ms	677×	body	2560	valid
286.0ms	324×	body	5120	valid
163.0ms	317×	body	640	valid
51.0ms	160×	body	320	valid
16.0ms	79×	body	160	valid