Details

sample74.0ms

Algorithm

intervals

Results

22.0ms	186×	body	80	valid
16.0ms	20×	body	5120	valid
9.0ms	14×	body	2560	valid
6.0ms	14×	body	640	valid
5.0ms	11×	body	1280	valid
3.0ms	10×	body	320	valid
0.0ms	1×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	31
3	31
2	29
1	24
0	12

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.3b

localize28.0ms

Local error

Found 1 expressions with local error:

0.7b	(+ (hypot re im) re)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity`
3×	`fma-def` `add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt`
1×	`expm1-log1p-u` `pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`

Counts

1 → 18

Calls

1 calls:

9.0ms

(+ (hypot re im) re)

series106.0ms

Counts

1 → 3

Calls

1 calls:

106.0ms

(+ (hypot re im) re)

simplify1.2s

Counts

21 → 21

Iterations

Iter	Nodes
5	2604
4	931
3	381
2	171
1	76
0	32

prune210.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.1b

localize32.0ms

Local error

Found 1 expressions with local error:

17.0b

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 11

Calls

1 calls:

0.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series213.0ms

Counts

1 → 3

Calls

1 calls:

213.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.5s

Counts

14 → 14

Iterations

Iter	Nodes
5	2584
4	924
3	284
2	96
1	47
0	26

prune145.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 13.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
16.9b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

rewrite5.0ms

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))
1.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

series580.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(cbrt (hypot re im))
135.0ms	(cbrt (hypot re im))
140.0ms	(cbrt (hypot re im))
190.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

simplify1.9s

Counts

65 → 65

Iterations

Iter	Nodes
5	3977
4	1250
3	461
2	171
1	83
0	51

prune621.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 13.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
17.0b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) re)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

46×	`cbrt-prod`
40×	`add-sqr-sqrt`
20×	`sqrt-prod`
18×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1` `swap-sqr`
9×	`associate-r` `associate-l` `unswap-sqr`
8×	`pow1/3`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 98

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
10.0ms	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
0.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) re)

series625.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (hypot re im))
177.0ms	(cbrt (hypot re im))
143.0ms	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
165.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) re)

simplify1.1s

Counts

110 → 110

Iterations

Iter	Nodes
4	2395
3	940
2	382
1	184
0	102

prune975.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.0b

regimes232.0ms

Accuracy

0% (0.2b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	12
1	12
0	9

end0.0ms

sample2.9s

Algorithm

intervals

Results

867.0ms	6005×	body	80	valid
722.0ms	479×	body	1280	valid
597.0ms	677×	body	2560	valid
292.0ms	301×	body	5120	valid
156.0ms	283×	body	640	valid
58.0ms	167×	body	320	valid
40.0ms	88×	body	160	valid