Details

Time bar (total: 23.8s)

sample92.0ms

Algorithm
intervals
Results
29.0ms200×body80valid
20.0ms22×body2560valid
10.0ms9×body5120valid
10.0ms13×body1280valid
5.0ms9×body640valid
1.0ms3×body320valid

simplify78.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
78.0ms
(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.1b

localize20.0ms

Local error

Found 2 expressions with local error:

0.4b
(+ (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)

series350.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
272.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
77.0ms
(+ (hypot re im) re)

simplify1.6s

Counts
40 → 40
Calls
40 calls:
Slowest
258.0ms
(* (* (+ (hypot re im) re) (+ (hypot re im) re)) (+ (hypot re im) re))
250.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
198.0ms
(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
136.0ms
(* (* (sqrt (* (+ (hypot re im) re) 2.0)) (sqrt (* (+ (hypot re im) re) 2.0))) (sqrt (* (+ (hypot re im) re) 2.0)))
107.0ms
(+ (* (hypot re im) (hypot re im)) (- (* re re) (* (hypot re im) re)))

prune435.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.9b

localize35.0ms

Local error

Found 4 expressions with local error:

13.7b
(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))
0.0b
(sqrt (hypot re im))
0.0b
(sqrt (hypot re im))

rewrite14.0ms

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
8.0ms
(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)

series851.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
376.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
216.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
134.0ms
(sqrt (hypot re im))
124.0ms
(sqrt (hypot re im))

simplify1.4s

Counts
71 → 69
Calls
71 calls:
Slowest
429.0ms
(* (* (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))
136.0ms
(* (* (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)))
66.0ms
(* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im)))
61.0ms
(expm1 (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
60.0ms
(* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im)))

prune746.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.9b

localize23.0ms

Local error

Found 4 expressions with local error:

13.7b
(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)))

rewrite22.0ms

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
12.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
3.0ms
(sqrt (sqrt (hypot re im)))
3.0ms
(sqrt (sqrt (hypot re im)))
0.0ms
(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re)

series689.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
210.0ms
(fma (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re)
168.0ms
(sqrt (sqrt (hypot re im)))
166.0ms
(sqrt (sqrt (hypot re im)))
145.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))

simplify3.7s

Counts
172 → 145
Calls
172 calls:
Slowest
676.0ms
(* (* (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))
231.0ms
(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
191.0ms
(* (* (* (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)))))
179.0ms
(+ (* 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)))))

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.9b

localize56.0ms

Local error

Found 4 expressions with local error:

13.7b
(fma (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re)
0.5b
(cbrt (hypot re im))
0.5b
(cbrt (hypot re im))
0.5b
(* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1
9×add-sqr-sqrt *-un-lft-identity add-cbrt-cube associate-*r* 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-*l* *-commutative fma-udef
Counts
4 → 69
Calls
4 calls:
Slowest
53.0ms
(* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im))))
2.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))
1.0ms
(fma (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re)

series780.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
267.0ms
(fma (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re)
187.0ms
(* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im))))
171.0ms
(cbrt (hypot re im))
155.0ms
(cbrt (hypot re im))

simplify6.4s

Counts
84 → 81
Calls
84 calls:
Slowest
595.0ms
(* (* (* (* (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))))) (sqrt (sqrt (hypot re im)))))
549.0ms
(* (* (* (* (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)))))) (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))))
455.0ms
(* (* (fma (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re) (fma (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re)) (fma (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re))
415.0ms
(* (* (* (* (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)))))) (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))))
339.0ms
(exp (fma (* (* (sqrt (fabs (cbrt (hypot re im)))) (sqrt (sqrt (cbrt (hypot re im))))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)) re))

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 10.9b

regimes266.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
847.0ms5969×body80valid
748.0ms517×body1280valid
721.0ms706×body2560valid
291.0ms301×body5120valid
130.0ms281×body640valid
53.0ms152×body320valid
19.0ms74×body160valid