Details

Time bar (total: 11.0s)

sample203.0ms

Algorithm
intervals
Results
30.0ms190×body80valid
21.0ms23×body2560valid
18.0ms16×body5120valid
13.0ms16×body1280valid
4.0ms7×body640valid
2.0ms2×body320valid
0.0ms2×body160valid

simplify112.0ms

Calls
1 calls:
Slowest
112.0ms
(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.6b

localize16.0ms

Local error

Found 2 expressions with local error:

0.7b
(- (hypot re im) re)
0.0b
(sqrt (* (- (hypot re im) re) 2.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity fma-neg add-cube-cbrt
2×expm1-log1p-u pow1 flip3-- add-cbrt-cube sqrt-div associate-*l/ add-exp-log insert-posit16 log1p-expm1-u flip-- add-log-exp
1×sub-neg pow1/2 sqrt-prod
Calls
2 calls:
Slowest
14.0ms
(- (hypot re im) re)
7.0ms
(sqrt (* (- (hypot re im) re) 2.0))

series198.0ms

Calls
2 calls:
Slowest
133.0ms
(sqrt (* (- (hypot re im) re) 2.0))
64.0ms
(- (hypot re im) re)

simplify622.0ms

Calls
11 calls:
Slowest
417.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
170.0ms
(sqrt (* (- (pow (hypot re im) 3) (pow re 3)) 2.0))
12.0ms
(sqrt (- (hypot re im) re))
7.0ms
(* (cbrt (hypot re im)) (cbrt (hypot re im)))
5.0ms
(sqrt (hypot re im))

prune268.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (hypot re im) re)
0.7b
(- (hypot re im) re)
0.4b
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
0.0b
(sqrt (- (hypot re im) re))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
14×sqrt-div
12×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
9×pow1 flip3-- sqrt-prod flip--
6×add-cbrt-cube fma-neg associate-*r* associate-*l* add-exp-log
5×pow1/2
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u add-log-exp
2×sub-neg pow-prod-down associate-*l/ associate-*r/ pow-prod-up
1×pow2 rem-sqrt-square rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
15.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
5.0ms
(sqrt (- (hypot re im) re))
4.0ms
(- (hypot re im) re)
4.0ms
(- (hypot re im) re)

series165.0ms

Calls
4 calls:
Slowest
63.0ms
(sqrt (- (hypot re im) re))
40.0ms
(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
34.0ms
(- (hypot re im) re)
28.0ms
(- (hypot re im) re)

simplify1.9s

Calls
56 calls:
Slowest
319.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (- (hypot re im) re)))
187.0ms
(sqrt (- (* (hypot re im) (hypot re im)) (* re re)))
180.0ms
(* (sqrt (- (pow (hypot re im) 3) (pow re 3))) (sqrt (- (* (hypot re im) (hypot re im)) (* re re))))
166.0ms
(* (sqrt (- (* (hypot re im) (hypot re im)) (* re re))) (sqrt (- (pow (hypot re im) 3) (pow re 3))))
160.0ms
(* (* (* (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))))

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.5b

localize19.0ms

Local error

Found 2 expressions with local error:

16.2b
(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))

rewrite4.0ms

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
3.0ms
(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))

series239.0ms

Calls
2 calls:
Slowest
155.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
84.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify22.0ms

Calls
7 calls:
Slowest
13.0ms
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
5.0ms
(- im re)
0.0ms
(- (+ re (- (+ (* +nan.0 (/ (pow im 2) (pow re 2))) (- +nan.0)))))
0.0ms
(- (+ (* +nan.0 (* (sqrt 2.0) (* re im))) (- (+ (* +nan.0 (* (sqrt 2.0) (pow im 2))) (- (* +nan.0 (* (sqrt 2.0) im)))))))
0.0ms
(- (+ re (- (+ (* +nan.0 (/ (pow im 2) (pow re 2))) (- +nan.0)))))

prune302.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.4b

localize12.0ms

Local error

Found 4 expressions with local error:

16.2b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
16.2b
(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 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log
5×pow1/2
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-prod-up fma-udef
1×pow2 rem-sqrt-square rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
9.0ms
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
2.0ms
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series370.0ms

Calls
4 calls:
Slowest
102.0ms
(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
100.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
97.0ms
(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
71.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify891.0ms

Calls
39 calls:
Slowest
260.0ms
(* (* (* (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)))))
116.0ms
(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
114.0ms
(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
27.0ms
(cbrt (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
26.0ms
(sqrt (cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.4b

regimes204.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
904.0ms6048×body80valid
858.0ms665×body2560valid
304.0ms312×body5120valid
273.0ms465×body1280valid
124.0ms301×body640valid
38.0ms130×body320valid
16.0ms79×body160valid