Details

sample69.0ms

Algorithm

intervals

Results

19.0ms	19×	body	2560	valid
16.0ms	190×	body	80	valid
11.0ms	18×	body	5120	valid
6.0ms	15×	body	1280	valid
3.0ms	7×	body	640	valid
2.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify57.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

57.0ms

(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.9b

localize26.0ms

Local error

Found 2 expressions with local error:

0.2b	(+ (hypot re im) re)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

Slowest

19.0ms	(+ (hypot re im) re)
12.0ms	(sqrt (* (+ (hypot re im) re) 2.0))

series361.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

284.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
76.0ms	(+ (hypot re im) re)

simplify552.0ms

Counts

15 → 40

Calls

15 calls:

Slowest

244.0ms	(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
201.0ms	(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
30.0ms	(* (+ (hypot re im) re) 2.0)
17.0ms	(* (exp (hypot re im)) (exp re))
16.0ms	(* (+ (hypot re im) re) 2.0)

prune393.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 12.7b

localize37.0ms

Local error

Found 2 expressions with local error:

16.3b	(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))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 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)

series557.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

330.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
227.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify71.0ms

Counts

9 → 31

Calls

9 calls:

Slowest

32.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
29.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
5.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
2.0ms	(+ re im)
0.0ms	(- re (+ (* +nan.0 (/ (pow im 2) (pow re 2))) (- +nan.0)))

prune326.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.6b

localize21.0ms

Local error

Found 4 expressions with local error:

16.0b	(fma (* (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))

rewrite3.0ms

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 (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

series705.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

185.0ms	(cbrt (hypot re im))
184.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)
168.0ms	(cbrt (hypot re im))
168.0ms	(cbrt (hypot re im))

simplify1.2s

Counts

21 → 65

Calls

21 calls:

Slowest

341.0ms	(cbrt 1)
223.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
222.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
173.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
31.0ms	(pow (/ 1 re) -1/3)

prune778.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.6b

localize42.0ms

Local error

Found 4 expressions with local error:

16.3b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
3.0b	(expm1 (log1p (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))))
0.0b	(log1p (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

Slowest

4.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
0.0ms	(log1p (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	(expm1 (log1p (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))))

series2.7s

Counts

4 → 12

Calls

4 calls:

Slowest

1.2s	(expm1 (log1p (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))))
884.0ms	(log1p (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
300.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
229.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify173.0ms

Counts

17 → 61

Calls

17 calls:

Slowest

48.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
39.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
33.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
29.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
9.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))

prune770.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.6b

regimes174.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch1.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

736.0ms	6040×	body	80	valid
736.0ms	303×	body	5120	valid
591.0ms	685×	body	2560	valid
327.0ms	474×	body	1280	valid
163.0ms	274×	body	640	valid
72.0ms	140×	body	320	valid
22.0ms	84×	body	160	valid