Details

sample137.0ms

Algorithm

intervals

Results

18.0ms	193×	body	80	valid
12.0ms	22×	body	2560	valid
7.0ms	9×	body	5120	valid
7.0ms	16×	body	1280	valid
4.0ms	12×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify76.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.1b	(- (hypot re im) re)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 45

Calls

2 calls:

12.0ms	(sqrt (* (- (hypot re im) re) 2.0))
10.0ms	(- (hypot re im) re)

series681.0ms

Counts

2 → 6

Calls

2 calls:

553.0ms	(sqrt (* (- (hypot re im) re) 2.0))
128.0ms	(- (hypot re im) re)

simplify2.3s

Counts

51 → 51

Iterations

Iter	Nodes
done	5001
3	1768
2	551
1	237
0	109

prune219.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 12.9b

localize43.0ms

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))
15.1b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

3.0ms	(sqrt (hypot re im))
3.0ms	(sqrt (hypot re im))
9.0ms	(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))

series888.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(sqrt (hypot re im))
136.0ms	(sqrt (hypot re im))
363.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
234.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify2.2s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	2087
2	565
1	207
0	97

prune468.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.1b	(sqrt (sqrt (hypot re im)))
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
15.0b	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

86×	`sqrt-prod`
54×	`add-sqr-sqrt`
40×	`sqrt-pow1`
31×	`pow1`
20×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 133

Calls

4 calls:

3.0ms	(sqrt (sqrt (hypot re im)))
3.0ms	(sqrt (sqrt (hypot re im)))
22.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

series621.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(sqrt (sqrt (hypot re im)))
134.0ms	(sqrt (sqrt (hypot re im)))
136.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
170.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

simplify1.8s

Counts

145 → 145

Iterations

Iter	Nodes
done	5000
3	1550
2	591
1	282
0	136

prune680.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.9b

localize94.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im))))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
15.0b	(fma (sqrt (hypot re im)) (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im)))) (- re))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
9×	`add-sqr-sqrt` `-un-lft-identity` `add-cbrt-cube` `associate-r*` `add-exp-log` `add-cube-cbrt` `sqrt-prod`
7×	`pow-prod-down`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod`
2×	`pow1/3` `sqrt-unprod`
1×	`associate-l` `*-commutative` `fma-udef`

Counts

4 → 69

Calls

4 calls:

97.0ms	(* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im))))
2.0ms	(cbrt (hypot re im))
2.0ms	(cbrt (hypot re im))
1.0ms	(fma (sqrt (hypot re im)) (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im)))) (- re))

series1.2s

Counts

4 → 12

Calls

4 calls:

644.0ms	(* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im))))
163.0ms	(cbrt (hypot re im))
159.0ms	(cbrt (hypot re im))
209.0ms	(fma (sqrt (hypot re im)) (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im)))) (- re))

simplify2.8s

Counts

81 → 81

Iterations

Iter	Nodes
done	5007
3	3590
2	1068
1	351
0	147

prune802.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.9b

regimes354.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.9b and baseline of 13.1b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.2s	6048×	body	80	valid
404.0ms	705×	body	2560	valid
283.0ms	477×	body	1280	valid
175.0ms	298×	body	5120	valid
80.0ms	275×	body	640	valid
29.0ms	141×	body	320	valid
9.0ms	56×	body	160	valid