Details

Time bar (total: 7.8s)

sample64.0ms

Algorithm
intervals
Results
19.0ms194×body80valid
14.0ms23×body2560valid
9.0ms16×body1280valid
6.0ms8×body5120valid
3.0ms7×body640valid
2.0ms8×body320valid

simplify51.0ms

Calls
1 calls:
Slowest
51.0ms
(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.1b

localize22.0ms

Local error

Found 2 expressions with local error:

0.3b
(+ (hypot re im) re)
0.2b
(sqrt (* (+ (hypot re im) re) 2.0))

rewrite6.0ms

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

series144.0ms

Calls
2 calls:
Slowest
105.0ms
(sqrt (* (+ (hypot re im) re) 2.0))
39.0ms
(+ (hypot re im) re)

simplify321.0ms

Calls
11 calls:
Slowest
243.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
57.0ms
(sqrt (* (+ (pow (hypot re im) 3) (pow re 3)) 2.0))
5.0ms
(* (cbrt (hypot re im)) (cbrt (hypot re im)))
4.0ms
(sqrt (+ (hypot re im) re))
3.0ms
(* 2 re)

prune321.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.4b
(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
0.3b
(+ (hypot re im) re)
0.0b
(sqrt (+ (hypot re im) re))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×associate-*l* sqrt-prod
5×pow1 add-cbrt-cube add-exp-log
4×sqrt-div
3×expm1-log1p-u fma-def flip3-+ pow1/2 associate-*r* flip-+ insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/
1×+-commutative rem-sqrt-square sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
3 calls:
Slowest
10.0ms
(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
6.0ms
(sqrt (+ (hypot re im) re))
3.0ms
(+ (hypot re im) re)

series225.0ms

Calls
3 calls:
Slowest
97.0ms
(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
90.0ms
(sqrt (+ (hypot re im) re))
38.0ms
(+ (hypot re im) re)

simplify824.0ms

Calls
32 calls:
Slowest
346.0ms
(* (* (* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re))) (sqrt (+ (hypot re im) re))) (* (* (sqrt 2.0) (sqrt 2.0)) (sqrt 2.0)))
151.0ms
(sqrt (- (* (hypot re im) (hypot re im)) (* re re)))
118.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt 2.0))
30.0ms
(* (+ (hypot re im) re) 2.0)
28.0ms
(* (sqrt (+ (pow (hypot re im) 3) (pow re 3))) (sqrt 2.0))

prune612.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.6b

localize13.0ms

Local error

Found 2 expressions with local error:

15.0b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.2b
(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)

series244.0ms

Calls
2 calls:
Slowest
136.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
108.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify18.0ms

Calls
7 calls:
Slowest
9.0ms
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
5.0ms
(+ 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
(- re (+ (* +nan.0 (/ (pow im 2) (pow re 2))) (- +nan.0)))

prune353.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.6b

localize28.0ms

Local error

Found 3 expressions with local error:

6.6b
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.2b
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt sqrt-prod
6×associate-*r* associate-*l*
5×add-cbrt-cube pow1/2 add-exp-log
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×flip3-+ sqrt-div pow-prod-down associate-*l/ pow-prod-up flip-+
1×pow2 +-commutative rem-square-sqrt fma-def pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
3 calls:
Slowest
14.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
10.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
5.0ms
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))

series168.0ms

Calls
3 calls:
Slowest
112.0ms
(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
31.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
25.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify667.0ms

Calls
34 calls:
Slowest
364.0ms
(sqrt (* (- (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (* re re)) 2.0))
114.0ms
(sqrt (* (+ (pow (* (sqrt (hypot re im)) (sqrt (hypot re im))) 3) (pow re 3)) 2.0))
47.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
15.0ms
(sqrt (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re))
12.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

prune689.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.6b

regimes214.0ms

Accuracy

0% (0.3b remaining)

Error of 12.8b against oracle of 12.5b and baseline of 12.8b

bsearch3.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.2s6089×body80valid
472.0ms630×body2560valid
349.0ms472×body1280valid
314.0ms283×body5120valid
145.0ms283×body640valid
48.0ms159×body320valid
17.0ms84×body160valid