Details

sample60.0ms

Algorithm

intervals

Results

18.0ms	192×	body	80	valid
17.0ms	29×	body	2560	valid
6.0ms	15×	body	1280	valid
5.0ms	7×	body	5120	valid
3.0ms	6×	body	640	valid
2.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify60.0ms

Calls

1 calls:

Slowest

59.0ms

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b	(+ (hypot re im) re)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

4.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
3.0ms	(+ (hypot re im) re)

series153.0ms

Calls

2 calls:

Slowest

108.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
45.0ms	(+ (hypot re im) re)

simplify341.0ms

Calls

11 calls:

Slowest

249.0ms	(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
54.0ms	(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
9.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
7.0ms	(sqrt (+ (hypot re im) re))
6.0ms	(* 2 re)

prune316.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.0b

localize15.0ms

Local error

Found 2 expressions with local error:

15.7b	(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))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

2.0ms	(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)

series230.0ms

Calls

2 calls:

Slowest

139.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
91.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify9.0ms

Calls

7 calls:

Slowest

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)))
0.0ms	(- (+ (* +nan.0 (sqrt 2.0)) (- (+ (* +nan.0 (/ (sqrt 2.0) re)) (- (* +nan.0 (/ (sqrt 2.0) (pow re 2))))))))
0.0ms	(- (+ (* +nan.0 (* (sqrt 2.0) (pow re 2))) (- (+ (* +nan.0 (* (sqrt 2.0) im)) (- (* +nan.0 (* (sqrt 2.0) re)))))))

prune313.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.9b

localize26.0ms

Local error

Found 4 expressions with local error:

15.5b	(fma (* (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))

rewrite2.0ms

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`

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)

series453.0ms

Calls

4 calls:

Slowest

120.0ms	(cbrt (hypot re im))
114.0ms	(cbrt (hypot re im))
111.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)
109.0ms	(cbrt (hypot re im))

simplify428.0ms

Calls

21 calls:

Slowest

126.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
93.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
87.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
14.0ms	(pow (/ 1 re) -1/3)
9.0ms	(cbrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))

prune836.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.8b

localize27.0ms

Local error

Found 4 expressions with local error:

15.5b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) re)
0.5b	(cbrt (sqrt (hypot re im)))
0.5b	(cbrt (sqrt (hypot re im)))
0.5b	(cbrt (hypot re im))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-prod`
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`

Calls

4 calls:

Slowest

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

series452.0ms

Calls

4 calls:

Slowest

126.0ms	(cbrt (sqrt (hypot re im)))
116.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) re)
107.0ms	(cbrt (sqrt (hypot re im)))
104.0ms	(cbrt (hypot re im))

simplify459.0ms

Calls

27 calls:

Slowest

110.0ms	(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
109.0ms	(+ (* 1/12 (* (pow re 2) (pow (/ 1 (pow im 11)) 1/6))) (pow im 1/6))
91.0ms	(+ (* 1/12 (* (pow re 2) (pow (/ 1 (pow im 11)) 1/6))) (pow im 1/6))
15.0ms	(pow (/ 1 re) -1/6)
15.0ms	(pow (/ 1 re) -1/6)

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 13.8b

regimes279.0ms

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 13.5b

bsearch1.0ms

end0.0ms

sample2.6s

Algorithm

intervals

Results

980.0ms	699×	body	2560	valid
775.0ms	5941×	body	80	valid
298.0ms	358×	body	5120	valid
253.0ms	498×	body	1280	valid
135.0ms	279×	body	640	valid
43.0ms	147×	body	320	valid
14.0ms	78×	body	160	valid