Details

sample296.0ms

Algorithm

intervals

Results

15.0ms	180×	body	80	valid
10.0ms	22×	body	2560	valid
8.0ms	13×	body	5120	valid
7.0ms	18×	body	1280	valid
4.0ms	14×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify84.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	12	15
1	19	10
2	28	10
3	36	10
4	43	10
5	45	10
done	45	10

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize17.0ms

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)

rewrite41.0ms

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×	`add-exp-log` `expm1-log1p-u` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `sqrt-pow1` `sqrt-div` `associate-*l/` `flip--`
1×	`sub-neg` `hypot-udef` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 53

Calls

3 calls:

18.0ms	(sqrt (* (- (hypot re im) re) 2.0))
1.0ms	(hypot re im)
18.0ms	(- (hypot re im) re)

series648.0ms

Counts

3 → 9

Calls

3 calls:

436.0ms	(sqrt (* (- (hypot re im) re) 2.0))
86.0ms	(hypot re im)
125.0ms	(- (hypot re im) re)

simplify3.1s

Counts

62 → 62

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	115	686
1	232	572
2	519	489
3	1765	434
done	5000	423

prune283.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 15.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (expm1 (log1p (- (hypot re im) re))) 2.0))
0.0b	(hypot re im)
0.9b	(- (hypot re im) re)
3.4b	(expm1 (log1p (- (hypot re im) re)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`pow1`
6×	`add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
2×	`sqrt-pow1`
1×	`sub-neg` `expm1-log1p` `hypot-udef` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip--` `distribute-lft-out--` `expm1-udef` `difference-of-squares`

Counts

4 → 62

Calls

4 calls:

10.0ms	(sqrt (* (expm1 (log1p (- (hypot re im) re))) 2.0))
1.0ms	(hypot re im)
21.0ms	(- (hypot re im) re)
1.0ms	(expm1 (log1p (- (hypot re im) re)))

series777.0ms

Counts

4 → 12

Calls

4 calls:

374.0ms	(sqrt (* (expm1 (log1p (- (hypot re im) re))) 2.0))
80.0ms	(hypot re im)
90.0ms	(- (hypot re im) re)
233.0ms	(expm1 (log1p (- (hypot re im) re)))

simplify3.2s

Counts

74 → 74

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	141	849
1	289	682
2	662	575
3	2369	511
done	5000	495

prune316.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 15.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
18.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 53

Calls

4 calls:

3.0ms	(sqrt (hypot re im))
3.0ms	(sqrt (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))

series803.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(sqrt (hypot re im))
113.0ms	(sqrt (hypot re im))
371.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
197.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify5.4s

Counts

65 → 65

Iterations

Useful iterations: 4 (3.7s)

Iter	Nodes	Cost
0	93	753
1	201	559
2	507	486
3	1529	465
4	4452	460
done	5000	460

prune321.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 15.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
18.5b	(fma (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (- re))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

14.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (- re))

series728.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))
179.0ms	(cbrt (hypot re im))
147.0ms	(cbrt (hypot re im))
251.0ms	(fma (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (- re))

simplify3.1s

Counts

76 → 76

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	136	1064
1	293	1010
2	867	914
3	2653	884
done	5000	882

prune505.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 15.0b

regimes185.0ms

Accuracy

0% (0.2b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	11	10
done	11	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.0s	6068×	body	80	valid
425.0ms	711×	body	2560	valid
224.0ms	450×	body	1280	valid
215.0ms	285×	body	5120	valid
62.0ms	238×	body	640	valid
33.0ms	167×	body	320	valid
11.0ms	81×	body	160	valid