Details

Time bar (total: 23.1s)

sample79.0ms

Algorithm
intervals
Results
24.0ms190×body80valid
16.0ms21×body2560valid
15.0ms22×body1280valid
7.0ms13×body640valid
4.0ms4×body5120valid
2.0ms5×body320valid
0.0ms1×body160valid

simplify30.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
29.0ms
(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.9b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

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
6.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
4.0ms
(+ (hypot re im) re)

series301.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
225.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
76.0ms
(+ (hypot re im) re)

simplify1.6s

Counts
40 → 40
Calls
40 calls:
Slowest
305.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
271.0ms
(* (* (+ (hypot re im) re) (+ (hypot re im) re)) (+ (hypot re im) re))
161.0ms
(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
141.0ms
(* (* (sqrt (* (+ (hypot re im) re) 2.0)) (sqrt (* (+ (hypot re im) re) 2.0))) (sqrt (* (+ (hypot re im) re) 2.0)))
98.0ms
(+ (pow (hypot re im) 3) (pow re 3))

prune384.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.7b

localize26.0ms

Local error

Found 4 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))
0.0b
(sqrt (hypot re im))
0.0b
(sqrt (hypot re im))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
8×add-sqr-sqrt
7×sqrt-prod
6×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/2
2×rem-sqrt-square
1×pow-prod-down fma-udef
Counts
4 → 57
Calls
4 calls:
Slowest
4.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
1.0ms
(sqrt (hypot re im))
1.0ms
(sqrt (hypot re im))
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series754.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
316.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
192.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
130.0ms
(sqrt (hypot re im))
116.0ms
(sqrt (hypot re im))

simplify1.3s

Counts
71 → 69
Calls
71 calls:
Slowest
377.0ms
(* (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
208.0ms
(* (* (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)) (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))) (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
60.0ms
(cbrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
54.0ms
(real->posit16 (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
52.0ms
(* (cbrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))) (cbrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))))

prune781.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 14.6b

localize28.0ms

Local error

Found 4 expressions with local error:

16.3b
(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)))

rewrite30.0ms

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
Counts
4 → 133
Calls
4 calls:
Slowest
16.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
4.0ms
(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re)
4.0ms
(sqrt (sqrt (hypot re im)))
3.0ms
(sqrt (sqrt (hypot re im)))

series647.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
213.0ms
(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re)
158.0ms
(sqrt (sqrt (hypot re im)))
144.0ms
(sqrt (sqrt (hypot re im)))
133.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))

simplify3.1s

Counts
172 → 145
Calls
172 calls:
Slowest
220.0ms
(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
218.0ms
(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
153.0ms
(* (* (* (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)))))
153.0ms
(* (* (* (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)))))
133.0ms
(* (* (fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re) (fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re)) (fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re))

prune1.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.6b

localize66.0ms

Local error

Found 4 expressions with local error:

16.2b
(fma (* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im)))))) (sqrt (hypot re im)) re)
0.5b
(cbrt (hypot re im))
0.5b
(cbrt (hypot re im))
0.5b
(* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1
9×add-sqr-sqrt *-un-lft-identity add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt sqrt-prod
7×pow-prod-down
6×cbrt-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-pow1 pow1/2 prod-exp cbrt-unprod
2×pow1/3 sqrt-unprod
1×associate-*r* *-commutative fma-udef
Counts
4 → 69
Calls
4 calls:
Slowest
37.0ms
(* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
0.0ms
(fma (* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im)))))) (sqrt (hypot re im)) re)

series757.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
225.0ms
(fma (* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im)))))) (sqrt (hypot re im)) re)
192.0ms
(* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))))
177.0ms
(cbrt (hypot re im))
162.0ms
(cbrt (hypot re im))

simplify6.9s

Counts
84 → 81
Calls
84 calls:
Slowest
581.0ms
(* (* (* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im)))))) (* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))))) (* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im)))))))
513.0ms
(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im)))))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im)))))))
482.0ms
(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (fabs (cbrt (hypot re im))))) (sqrt (fabs (cbrt (hypot re im))))) (* (* (sqrt (sqrt (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (cbrt (hypot re im)))))))
460.0ms
(+ (* (sqrt (fabs (pow (hypot re im) 1/3))) (pow im 1/3)) (* 1/6 (* (pow re 2) (* (sqrt (fabs (pow (hypot re im) 1/3))) (pow (/ 1 (pow im 5)) 1/3)))))
405.0ms
(exp (fma (* (sqrt (sqrt (hypot re im))) (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im)))))) (sqrt (hypot re im)) re))

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 14.5b

regimes277.0ms

Accuracy

0% (0.3b remaining)

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

bsearch1.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
835.0ms5981×body80valid
768.0ms478×body1280valid
613.0ms688×body2560valid
265.0ms318×body5120valid
158.0ms291×body640valid
52.0ms161×body320valid
18.0ms83×body160valid