Details

sample62.0ms

Algorithm

intervals

Results

17.0ms	195×	body	80	valid
11.0ms	10×	body	5120	valid
10.0ms	18×	body	2560	valid
7.0ms	15×	body	1280	valid
4.0ms	12×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify52.0ms

Counts: 1 → 1

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize29.0ms

Local error

Found 3 expressions with local error:

0.9b	(+ (hypot re im) re)
0.0b	(hypot re im)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))

rewrite18.0ms

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

9.0ms	(+ (hypot re im) re)
8.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
0.0ms	(hypot re im)

series387.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

252.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
75.0ms	(+ (hypot re im) re)
60.0ms	(hypot re im)

simplify1.9s

Counts: 54 → 54

prune544.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.6b

localize20.0ms

Local error

Found 4 expressions with local error:

14.9b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.0b	(hypot re im)
0.0b	(hypot re im)
0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))

rewrite5.0ms

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

4.0ms	(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)

series659.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

335.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
182.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
74.0ms	(hypot re im)
68.0ms	(hypot re im)

simplify1.3s

Counts: 59 → 59

prune729.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.6b

localize37.0ms

Local error

Found 4 expressions with local error:

14.9b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
14.9b	(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)

rewrite11.0ms

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

9.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.0ms	(hypot re im)

series675.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

212.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
203.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
199.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
61.0ms	(hypot re im)

simplify1.3s

Counts: 97 → 97

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.5b

localize41.0ms

Local error

Found 4 expressions with local error:

14.9b	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))

rewrite9.0ms

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

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

series683.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

178.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)
176.0ms	(cbrt (hypot re im))
173.0ms	(cbrt (hypot re im))
155.0ms	(cbrt (hypot re im))

simplify2.4s

Counts: 65 → 65

prune824.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.5b

regimes177.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch3.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

885.0ms	6000×	body	80	valid
723.0ms	499×	body	1280	valid
610.0ms	695×	body	2560	valid
304.0ms	325×	body	5120	valid
194.0ms	302×	body	640	valid
42.0ms	121×	body	320	valid
13.0ms	58×	body	160	valid