Details

sample78.0ms

Algorithm

intervals

Results

24.0ms	190×	body	80	valid
18.0ms	25×	body	2560	valid
15.0ms	16×	body	5120	valid
6.0ms	11×	body	1280	valid
4.0ms	7×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify44.0ms

Calls

1 calls:

Slowest

44.0ms

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.1b

localize25.0ms

Local error

Found 1 expressions with local error:

0.7b	(+ (hypot re im) re)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

1 calls:

Slowest

7.0ms

(+ (hypot re im) re)

series45.0ms

Calls

1 calls:

Slowest

45.0ms

(+ (hypot re im) re)

simplify27.0ms

Calls

5 calls:

Slowest

13.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
6.0ms	(sqrt (hypot re im))
3.0ms	(* 2 re)
3.0ms	(+ re im)
1.0ms	0

prune168.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 11.9b

localize24.0ms

Local error

Found 1 expressions with local error:

15.9b

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

rewrite0.0ms

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`

Calls

1 calls:

Slowest

0.0ms

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

series92.0ms

Calls

1 calls:

Slowest

92.0ms

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

simplify6.0ms

Calls

3 calls:

Slowest

4.0ms	(+ re im)
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)))

prune189.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.9b

localize25.0ms

Local error

Found 2 expressions with local error:

9.5b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
6×	`add-sqr-sqrt` `-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `pow1/2` `add-exp-log`
2×	`expm1-log1p-u` `pow-prod-down` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `+-commutative` `rem-square-sqrt` `fma-def` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Calls

2 calls:

Slowest

13.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
12.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

series71.0ms

Calls

2 calls:

Slowest

36.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
34.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify187.0ms

Calls

28 calls:

Slowest

65.0ms	(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
10.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
9.0ms	(+ (log (sqrt (hypot re im))) (log (sqrt (hypot re im))))
6.0ms	(+ 1 1)
6.0ms	(sqrt (hypot re im))

prune585.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.8b

localize29.0ms

Local error

Found 4 expressions with local error:

7.5b	(+ (* (fabs (cbrt (hypot re im))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))) re)
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.3b	(* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod` `associate-l` `sqrt-prod`
6×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow1/2` `pow1/3` `pow-prod-down`
1×	`+-commutative` `fma-def` `flip3-+` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Calls

4 calls:

Slowest

15.0ms	(+ (* (fabs (cbrt (hypot re im))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))) re)
13.0ms	(* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))

series453.0ms

Calls

4 calls:

Slowest

142.0ms	(* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))
112.0ms	(cbrt (hypot re im))
108.0ms	(cbrt (hypot re im))
91.0ms	(+ (* (fabs (cbrt (hypot re im))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))) re)

simplify1.0s

Calls

38 calls:

Slowest

346.0ms	(+ (* 1/3 (* (* (pow re 2) (fabs (pow (hypot re im) 1/3))) (pow (/ 1 (pow im 4)) 1/3))) (+ re (* (fabs (pow (hypot re im) 1/3)) (pow (pow im 2) 1/3))))
108.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
106.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
103.0ms	(* (* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
82.0ms	(+ (pow im 2/3) (* 1/3 (* (pow re 2) (pow (/ 1 (pow im 4)) 1/3))))

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.8b

regimes240.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch2.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

914.0ms	693×	body	2560	valid
823.0ms	6010×	body	80	valid
303.0ms	469×	body	1280	valid
234.0ms	299×	body	5120	valid
194.0ms	291×	body	640	valid
57.0ms	158×	body	320	valid
17.0ms	80×	body	160	valid