Details

sample190.0ms

Algorithm

intervals

Results

34.0ms	200×	body	80	valid
17.0ms	18×	body	2560	valid
14.0ms	13×	body	5120	valid
11.0ms	12×	body	1280	valid
4.0ms	6×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify141.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

140.0ms

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.5b

localize19.0ms

Local error

Found 1 expressions with local error:

0.8b	(- (hypot re im) re)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 29

Calls

1 calls:

Slowest

7.0ms

(- (hypot re im) re)

series84.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

84.0ms

(- (hypot re im) re)

simplify516.0ms

Counts

27 → 32

Calls

27 calls:

Slowest

69.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (cbrt re) (* (cbrt re) (cbrt re)))))
40.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* re 1)))
39.0ms	(fma 1 (hypot re im) (- (* (sqrt re) (sqrt re))))
36.0ms	(fma 1 (hypot re im) (- (* re 1)))
36.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (sqrt re) (sqrt re))))

prune275.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 10.3b

localize41.0ms

Local error

Found 1 expressions with local error:

13.5b

(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:

Slowest

1.0ms

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

series212.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

212.0ms

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

simplify4.0ms

Counts

3 → 14

Calls

3 calls:

Slowest

3.0ms	(- im re)
0.0ms	(- (+ re (- (+ (* +nan.0 (/ (pow im 2) (pow re 2))) (- +nan.0)))))
0.0ms	(- (+ re (- (+ (* +nan.0 (/ (pow im 2) (pow re 2))) (- +nan.0)))))

prune170.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.3b

localize59.0ms

Local error

Found 4 expressions with local error:

13.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
13.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
13.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.5b	(cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 47

Calls

4 calls:

Slowest

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

series948.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

296.0ms	(cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
240.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
225.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
187.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify240.0ms

Counts

15 → 59

Calls

15 calls:

Slowest

167.0ms	(- (+ (* 1/18 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3)) (* 1/3 (* re (pow (/ 1 (pow im 2)) 1/3))))
30.0ms	(cbrt (* (cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))))
24.0ms	(cbrt (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
3.0ms	(- im re)
3.0ms	(- im re)

prune897.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.3b

localize44.0ms

Local error

Found 4 expressions with local error:

13.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
13.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
13.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
13.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`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

4 → 44

Calls

4 calls:

Slowest

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	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series781.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

216.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
205.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
187.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
173.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify27.0ms

Counts

12 → 56

Calls

12 calls:

Slowest

5.0ms	(- im re)
5.0ms	(- im re)
5.0ms	(- im re)
3.0ms	(- im re)
0.0ms	(- (+ re (- (+ (* +nan.0 (/ (pow im 2) (pow re 2))) (- +nan.0)))))

prune775.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 10.3b

regimes243.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

868.0ms	6021×	body	80	valid
732.0ms	466×	body	1280	valid
597.0ms	709×	body	2560	valid
318.0ms	302×	body	5120	valid
152.0ms	271×	body	640	valid
80.0ms	154×	body	320	valid
17.0ms	77×	body	160	valid