Details

sample128.0ms

Algorithm

intervals

Results

18.0ms	197×	body	80	valid
9.0ms	19×	body	2560	valid
9.0ms	14×	body	5120	valid
6.0ms	15×	body	1280	valid
2.0ms	5×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify102.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

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: 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)

rewrite33.0ms

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:

1.0ms	(hypot re im)
19.0ms	(sqrt (* (- (hypot re im) re) 2.0))
9.0ms	(- (hypot re im) re)

series398.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(hypot re im)
261.0ms	(sqrt (* (- (hypot re im) re) 2.0))
82.0ms	(- (hypot re im) re)

simplify2.8s

Counts

62 → 62

Iterations

Useful iterations: done (2.8s)

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

prune210.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.2b

localize21.0ms

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))

rewrite13.0ms

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))
2.0ms	(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))

series804.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(sqrt (hypot re im))
149.0ms	(sqrt (hypot re im))
332.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
191.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify4.9s

Counts

65 → 65

Iterations

Useful iterations: 4 (3.5s)

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

prune377.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.1b

localize29.0ms

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 (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

rewrite41.0ms

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:

5.0ms	(sqrt (sqrt (hypot re im)))
3.0ms	(sqrt (sqrt (hypot re im)))
23.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.0ms	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

series716.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(sqrt (sqrt (hypot re im)))
191.0ms	(sqrt (sqrt (hypot re im)))
129.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
208.0ms	(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

simplify4.2s

Counts

141 → 141

Iterations

Useful iterations: 4 (2.2s)

Iter	Nodes	Cost
0	132	1875
1	246	1020
2	590	942
3	1488	921
4	4300	907
done	5000	907

prune566.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 11.1b

localize43.0ms

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 (* (* (fabs (cbrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (cbrt (sqrt (hypot re im))))) (sqrt (hypot re im)) (- re))

rewrite47.0ms

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:

37.0ms	(* (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 (* (* (fabs (cbrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (cbrt (sqrt (hypot re im))))) (sqrt (hypot re im)) (- re))

series860.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (fabs (cbrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
207.0ms	(cbrt (sqrt (hypot re im)))
157.0ms	(cbrt (sqrt (hypot re im)))
293.0ms	(fma (* (* (fabs (cbrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (cbrt (sqrt (hypot re im))))) (sqrt (hypot re im)) (- re))

simplify3.3s

Counts

82 → 82

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	150	1336
1	326	1273
2	879	1116
3	2642	1086
done	5000	1086

prune520.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 11.1b

regimes97.0ms

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

sample1.8s

Algorithm

intervals

Results

647.0ms	6047×	body	80	valid
326.0ms	655×	body	2560	valid
203.0ms	495×	body	1280	valid
184.0ms	286×	body	5120	valid
111.0ms	278×	body	640	valid
28.0ms	144×	body	320	valid
12.0ms	95×	body	160	valid