Details

sample70.0ms

Algorithm

intervals

Results

20.0ms	33×	body	2560	valid
18.0ms	191×	body	80	valid
8.0ms	15×	body	1280	valid
3.0ms	5×	body	5120	valid
3.0ms	6×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid

simplify54.0ms

Counts: 1 → 1

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.7b

localize30.0ms

Local error

Found 3 expressions with local error:

0.7b	(+ (hypot re im) re)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.0b	(hypot re im)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `*-un-lft-identity`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`+-commutative` `hypot-udef` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

3 → 45

Calls

3 calls:

Slowest

13.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
9.0ms	(+ (hypot re im) re)
0.0ms	(hypot re im)

series453.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

279.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
110.0ms	(+ (hypot re im) re)
63.0ms	(hypot re im)

simplify1.8s

Counts: 54 → 54

prune725.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.5b

localize48.0ms

Local error

Found 4 expressions with local error:

16.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
0.0b	(hypot re im)
0.0b	(hypot re im)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

Slowest

7.0ms	(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)
0.0ms	(hypot re im)
0.0ms	(hypot re im)

series684.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

325.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
238.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
67.0ms	(hypot re im)
54.0ms	(hypot re im)

simplify1.4s

Counts: 59 → 59

prune783.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.5b

localize62.0ms

Local error

Found 4 expressions with local error:

16.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
16.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.4b	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
0.0b	(hypot re im)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`fma-udef`
1×	`pow2` `hypot-udef` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

Slowest

18.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.0ms	(hypot re im)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series748.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

253.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
215.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
208.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
72.0ms	(hypot re im)

simplify1.4s

Counts: 97 → 97

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.5b

localize86.0ms

Local error

Found 4 expressions with local error:

15.9b	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))

rewrite6.0ms

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:

Slowest

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

series655.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

186.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)
168.0ms	(cbrt (hypot re im))
164.0ms	(cbrt (hypot re im))
137.0ms	(cbrt (hypot re im))

simplify751.0ms

Counts: 65 → 65

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.5b

regimes241.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.1b and baseline of 13.3b

bsearch3.0ms

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	6027×	body	80	valid
631.0ms	697×	body	2560	valid
348.0ms	512×	body	1280	valid
234.0ms	271×	body	5120	valid
155.0ms	252×	body	640	valid
87.0ms	154×	body	320	valid
41.0ms	87×	body	160	valid