Details

Time bar (total: 15.4s)

sample57.0ms

Algorithm
intervals
Results
15.0ms192×body80valid
12.0ms25×body2560valid
11.0ms9×body640valid
8.0ms20×body1280valid
3.0ms6×body5120valid
0.0ms3×body160valid
0.0ms1×body320valid

simplify36.0ms

Calls
1 calls:
Slowest
36.0ms
(* 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: 13.2b

localize38.0ms

Local error

Found 2 expressions with local error:

0.6b
(+ (hypot re im) re)
0.0b
(sqrt (* (+ (hypot re im) re) 2.0))

rewrite22.0ms

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
Calls
2 calls:
Slowest
13.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
9.0ms
(+ (hypot re im) re)

series384.0ms

Calls
2 calls:
Slowest
300.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
84.0ms
(+ (hypot re im) re)

simplify498.0ms

Calls
15 calls:
Slowest
218.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
204.0ms
(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
19.0ms
(* (+ (hypot re im) re) 2.0)
16.0ms
(* (+ (hypot re im) re) 2.0)
8.0ms
(* (exp (hypot re im)) (exp re))

prune315.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (hypot re im) re)
0.6b
(+ (hypot re im) re)
0.4b
(* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re)))
0.0b
(sqrt (+ (hypot re im) re))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
30×add-sqr-sqrt sqrt-prod
20×pow1
15×add-cube-cbrt
14×sqrt-div
11×swap-sqr
9×sqrt-pow1 flip3-+ pow1/2 flip-+ distribute-lft-out
8×add-log-exp
7×associate-*r* associate-*l*
6×fma-def add-cbrt-cube add-exp-log
5×pow-prod-up
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u unswap-sqr
3×pow-prod-down pow-sqr
2×+-commutative sum-log associate-*l/ associate-*r/
1×pow2 rem-sqrt-square rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod hypot-def
Calls
4 calls:
Slowest
34.0ms
(* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re)))
10.0ms
(sqrt (+ (hypot re im) re))
4.0ms
(+ (hypot re im) re)
4.0ms
(+ (hypot re im) re)

series373.0ms

Calls
4 calls:
Slowest
156.0ms
(sqrt (+ (hypot re im) re))
84.0ms
(+ (hypot re im) re)
72.0ms
(+ (hypot re im) re)
60.0ms
(* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re)))

simplify3.6s

Calls
109 calls:
Slowest
373.0ms
(* (sqrt (+ (pow (hypot re im) 3) (pow re 3))) (sqrt (+ (hypot re im) re)))
317.0ms
(* (sqrt (+ (pow (hypot re im) 3) (pow re 3))) (sqrt (+ (pow (hypot re im) 3) (pow re 3))))
275.0ms
(* (* (* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re))) (sqrt (+ (hypot re im) re))) (* (* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re))) (sqrt (+ (hypot re im) re))))
254.0ms
(* (sqrt (+ (pow (hypot re im) 3) (pow re 3))) (sqrt (- (* (hypot re im) (hypot re im)) (* re re))))
230.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (+ (pow (hypot re im) 3) (pow re 3))))

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 13.1b

localize27.0ms

Local error

Found 4 expressions with local error:

15.6b
(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
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)

series1.2s

Calls
4 calls:
Slowest
654.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
362.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
116.0ms
(sqrt (hypot re im))
111.0ms
(sqrt (hypot re im))

simplify123.0ms

Calls
25 calls:
Slowest
40.0ms
(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
28.0ms
(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)
9.0ms
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
7.0ms
(sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im))))
7.0ms
(sqrt (sqrt (hypot re im)))

prune707.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 13.0b

localize45.0ms

Local error

Found 4 expressions with local error:

15.6b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
15.6b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.5b
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
0.0b
(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) 2.0))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
25×pow1
24×add-sqr-sqrt
19×sqrt-prod
12×*-un-lft-identity add-cube-cbrt
11×sqrt-pow1
9×pow1/2
8×swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* pow-prod-down add-exp-log
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow-sqr
2×fma-udef
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
40.0ms
(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) 2.0))
17.0ms
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
1.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series924.0ms

Calls
4 calls:
Slowest
318.0ms
(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) 2.0))
210.0ms
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
200.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
196.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.4s

Calls
77 calls:
Slowest
242.0ms
(* (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))))
102.0ms
(* (* (cbrt (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) (cbrt (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))) (* (cbrt (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) (cbrt (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))))
84.0ms
(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
68.0ms
(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
57.0ms
(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))

prune1.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.0b

regimes193.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch1.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
936.0ms6049×body80valid
567.0ms696×body2560valid
390.0ms491×body1280valid
274.0ms292×body5120valid
124.0ms250×body640valid
81.0ms137×body320valid
43.0ms85×body160valid