Details

sample92.0ms

Algorithm

intervals

Results

14.0ms	197×	body	80	valid
7.0ms	19×	body	2560	valid
6.0ms	14×	body	5120	valid
5.0ms	15×	body	1280	valid
1.0ms	5×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify78.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (8.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.8b	(- (hypot re im) re)

rewrite25.0ms

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:

0.0ms	(hypot re im)
12.0ms	(sqrt (* (- (hypot re im) re) 2.0))
10.0ms	(- (hypot re im) re)

series340.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(hypot re im)
205.0ms	(sqrt (* (- (hypot re im) re) 2.0))
85.0ms	(- (hypot re im) re)

simplify2.7s

Counts

62 → 62

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	115	686
1	232	572
2	519	489
3	1768	434
done	5000	423

prune206.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.2b

localize14.0ms

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))
14.6b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite9.0ms

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:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
5.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series770.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(sqrt (hypot re im))
106.0ms	(sqrt (hypot re im))
340.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
216.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify5.0s

Counts

65 → 65

Iterations

Useful iterations: 4 (3.6s)

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

prune337.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.1b

localize35.0ms

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))))
14.5b	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

3.0ms	(sqrt (sqrt (hypot re im)))
2.0ms	(sqrt (sqrt (hypot re im)))
21.0ms	(* (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))

series674.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(sqrt (sqrt (hypot re im)))
156.0ms	(sqrt (sqrt (hypot re im)))
135.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
213.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

simplify4.1s

Counts

141 → 141

Iterations

Useful iterations: 4 (2.3s)

Iter	Nodes	Cost
0	132	1875
1	246	1020
2	590	942
3	1487	921
4	4271	907
done	5000	907

prune428.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 11.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (fabs (cbrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
0.5b	(cbrt (sqrt (hypot re im)))
0.5b	(cbrt (sqrt (hypot re im)))
14.6b	(fma (sqrt (hypot re im)) (* (* (fabs (cbrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (cbrt (sqrt (hypot re im))))) (- re))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `sqrt-prod`
12×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
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 → 70

Calls

4 calls:

35.0ms	(* (fabs (cbrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
3.0ms	(cbrt (sqrt (hypot re im)))
3.0ms	(cbrt (sqrt (hypot re im)))
1.0ms	(fma (sqrt (hypot re im)) (* (* (fabs (cbrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (cbrt (sqrt (hypot re im))))) (- re))

series825.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (fabs (cbrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
174.0ms	(cbrt (sqrt (hypot re im)))
189.0ms	(cbrt (sqrt (hypot re im)))
276.0ms	(fma (sqrt (hypot re im)) (* (* (fabs (cbrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (cbrt (sqrt (hypot re im))))) (- re))

simplify2.3s

Counts

82 → 82

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	147	1315
1	314	1253
2	815	1103
3	2304	1086
done	5000	1074

prune563.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 11.1b

regimes118.0ms

Accuracy

0% (0.2b remaining)

Error of 13.2b against oracle of 13.0b and baseline of 13.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.6s

Algorithm

intervals

Results

501.0ms	6047×	body	80	valid
302.0ms	655×	body	2560	valid
273.0ms	495×	body	1280	valid
199.0ms	286×	body	5120	valid
103.0ms	278×	body	640	valid
25.0ms	144×	body	320	valid
11.0ms	95×	body	160	valid