Details

Time bar (total: 24.3s)

sample179.0ms

Algorithm
intervals
Results
28.0ms201×body80valid
17.0ms22×body2560valid
7.0ms12×body1280valid
5.0ms6×body5120valid
4.0ms9×body640valid
2.0ms4×body320valid
0.0ms2×body160valid

simplify147.0ms

Calls
1 calls:
Slowest
147.0ms
(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize29.0ms

Local error

Found 2 expressions with local error:

0.4b
(- (hypot re im) re)
0.0b
(sqrt (* (- (hypot re im) re) 2.0))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×*-un-lft-identity
14×sqrt-prod
12×add-cube-cbrt
9×prod-diff
5×pow1 associate-*l*
4×add-log-exp
3×fma-neg associate-*r*
2×expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-- add-cbrt-cube sqrt-div associate-*l/ add-exp-log insert-posit16 log1p-expm1-u flip-- distribute-lft-out-- difference-of-squares unswap-sqr
1×sub-neg pow1/2 diff-log pow-prod-down *-commutative
Calls
2 calls:
Slowest
39.0ms
(sqrt (* (- (hypot re im) re) 2.0))
21.0ms
(- (hypot re im) re)

series371.0ms

Calls
2 calls:
Slowest
264.0ms
(sqrt (* (- (hypot re im) re) 2.0))
106.0ms
(- (hypot re im) re)

simplify1.4s

Calls
50 calls:
Slowest
220.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
148.0ms
(sqrt (* (- (pow (hypot re im) 3) (pow re 3)) 2.0))
111.0ms
(sqrt (* (- (hypot re im) re) (* (cbrt 2.0) (cbrt 2.0))))
64.0ms
(sqrt (sqrt (* (- (hypot re im) re) 2.0)))
53.0ms
(sqrt (* (- (hypot re im) re) (sqrt 2.0)))

prune661.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (hypot re im) re)
0.4b
(- (hypot re im) re)
0.4b
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
0.0b
(sqrt (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 2.0))

rewrite303.0ms

Algorithm
rewrite-expression-head
Rules
138×add-sqr-sqrt
132×sqrt-prod
69×*-un-lft-identity
53×associate-*l*
38×unswap-sqr
37×add-cube-cbrt
32×sqrt-div swap-sqr
25×pow1
19×associate-*r*
18×prod-diff
14×flip3-- flip-- distribute-lft-out--
12×rem-sqrt-square associate-*l/
11×sqrt-pow1
10×difference-of-squares
9×pow1/2
8×frac-times add-log-exp
6×add-cbrt-cube fma-neg pow-prod-down add-exp-log
5×*-commutative pow-prod-up
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u
3×pow-sqr
2×sub-neg diff-log
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp cbrt-unprod
Calls
4 calls:
Slowest
222.0ms
(sqrt (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 2.0))
55.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
9.0ms
(- (hypot re im) re)
9.0ms
(- (hypot re im) re)

series578.0ms

Calls
4 calls:
Slowest
309.0ms
(sqrt (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 2.0))
97.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
93.0ms
(- (hypot re im) re)
78.0ms
(- (hypot re im) re)

simplify8.4s

Calls
223 calls:
Slowest
343.0ms
(sqrt (* (* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt (- (pow (hypot re im) 3) (pow re 3)))) 2.0))
327.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (- (hypot re im) re)))
324.0ms
(sqrt (* (* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (- (pow (hypot re im) 3) (pow re 3)))) 2.0))
315.0ms
(* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt (- (* (hypot re im) (hypot re im)) (* re re))))
297.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (- (pow (hypot re im) 3) (pow re 3))))

prune2.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 12.6b

localize17.0ms

Local error

Found 4 expressions with local error:

13.2b
(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))
0.0b
(sqrt (hypot re im))
0.0b
(sqrt (hypot re im))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-prod
16×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/2 associate-*r* associate-*l*
2×unswap-sqr
1×pow-prod-down *-commutative fma-udef
Calls
4 calls:
Slowest
13.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
2.0ms
(sqrt (hypot re im))
2.0ms
(sqrt (hypot re im))
1.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series757.0ms

Calls
4 calls:
Slowest
361.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
202.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
104.0ms
(sqrt (hypot re im))
90.0ms
(sqrt (hypot re im))

simplify731.0ms

Calls
38 calls:
Slowest
110.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) (* (cbrt 2.0) (cbrt 2.0))))
72.0ms
(sqrt (* (cbrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)) (cbrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))))
71.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
70.0ms
(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)
65.0ms
(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))

prune914.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.5b

localize22.0ms

Local error

Found 4 expressions with local error:

13.2b
(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))
0.5b
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.1b
(sqrt (sqrt (hypot re im)))
0.1b
(sqrt (sqrt (hypot re im)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
86×sqrt-prod
54×add-sqr-sqrt
40×sqrt-pow1
31×pow1
20×*-un-lft-identity pow1/2 add-cube-cbrt
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×expm1-log1p-u rem-sqrt-square insert-posit16 log1p-expm1-u add-log-exp
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod fma-udef
Calls
4 calls:
Slowest
25.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
10.0ms
(sqrt (sqrt (hypot re im)))
3.0ms
(sqrt (sqrt (hypot re im)))
1.0ms
(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))

series652.0ms

Calls
4 calls:
Slowest
218.0ms
(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) (- re))
158.0ms
(sqrt (sqrt (hypot re im)))
147.0ms
(sqrt (sqrt (hypot re im)))
129.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))

simplify1.7s

Calls
140 calls:
Slowest
227.0ms
(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
203.0ms
(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
196.0ms
(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))))
70.0ms
(* (* (cbrt (sqrt (sqrt (hypot re im)))) (cbrt (sqrt (sqrt (hypot re im))))) (* (cbrt (sqrt (sqrt (hypot re im)))) (cbrt (sqrt (sqrt (hypot re im))))))
35.0ms
(pow (/ 1 re) -1/4)

prune1.8s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.5b

regimes287.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.3s6010×body80valid
533.0ms684×body2560valid
352.0ms295×body5120valid
269.0ms486×body1280valid
121.0ms279×body640valid
53.0ms163×body320valid
18.0ms83×body160valid